Aviation, Marine, Auto & Field Calculators

Exact rise, set, solar noon and day length for any place and date — the NOAA solar equations with the refraction fine print included.

Tonight's golden hour and blue hour, computed from sun elevation — the photographer's light windows with the angles that define them.

Hours of daylight for any date and latitude, how fast it's changing, and the swing between your solstices.

All three twilight boundaries for any date and place — when to stop flying VFR, when the horizon vanishes at sea, when the stars switch fully on.

Where exactly is the sun right now — elevation and compass azimuth for any time and place, for solar panels, shadows, photos and windows.

How long a shadow anything casts at any time and place — height ÷ tan(sun elevation), with the direction it falls and the solar-design uses.

Tonight's moon — phase name, illumination percent and age in days — for any date, with the next full and new moon.

The exact dates and times of both equinoxes and solstices for any year — Meeus polynomial accuracy, with what each moment actually means.

Two machines at 90 dB each ≠ 180 dB: add up to five incoherent sound sources the logarithmic way, with the +3/+10 rules explained.

Frequency to wavelength at the real speed of sound in your air — why bass is furniture-sized, treble is fingertip-sized, and rooms care.

Your room's bass problem, predicted: axial mode frequencies for all three dimensions, the pile-ups, and the ratios that spread them out.

Sound level at any distance from a source — the −6 dB-per-doubling law, hearing-safety bands, and why outdoor PA needs so much power.

Room volume + surface absorption → reverberation time, with material presets and the targets for studios, home theaters, classrooms and halls.

Any note to its frequency and back — MIDI numbers, cents offset, the 2^(1/12) math, and alternate concert pitches from 432 to 444.

Tempo into milliseconds: delay, reverb pre-delay and LFO times for every note division — straight, dotted and triplet — plus the Hz for synced LFOs.

Crossover frequency + driver impedances → the capacitor and inductor values for 1st and 2nd-order passive networks, with slope trade-offs explained.

Box volume + tuning frequency + port size → the port length that hits the note, with port-velocity chuffing checks and flare advice.

Great-circle distance between any two lat/long points — km, miles and nautical miles, with the initial bearing thrown in.

Initial and final bearings between two coordinates — why they differ on a round Earth, plus the compass-rose name of your heading.

Where do you end up? Start coordinates, a bearing and a distance → the destination lat/long, by exact great-circle math.

40°26′46″N to 40.4461 and back — both directions of the coordinate-format conversion every GPS, map and dataset eventually demands.

Latitude/longitude into UTM zone, easting and northing — the metre-gridded coordinates surveyors, soldiers and field scientists actually measure in.

Dig straight through: the exact opposite point of any coordinates — with why it's almost never China, and almost always ocean.

Paste a list of lat/long corners → field area in hectares, acres and m² by spherical polygon math, plus the perimeter walked.

Centre + radius → the circle's area, the lat/long bounding box for your database query, and the degree-deltas that make radius search fast.

How many kilometres is one degree — of latitude (almost constant) and longitude (shrinks to zero) — at any latitude on Earth.

1:50,000 decoded — convert between map distance, ground distance and scale ratio, with the cm-per-km mental math and area-scaling trap.

Near limit, far limit and total DoF for any lens, aperture, distance and sensor — with the hyperfocal connection and the background-blur truth.

Focus here and everything from half this distance to infinity is acceptably sharp — the landscape photographer's most useful number, per lens and sensor.

What your lens 'really is' on any sensor: equivalent focal length, equivalent aperture for DoF, and the light-gathering truth behind the equivalence wars.

Horizontal, vertical and diagonal angles plus scene width at any distance — what the lens actually sees, for any focal length and sensor.

Change one side, rebalance another: aperture, shutter and ISO traded in exact stops, with the EV they all add up to.

ND8, ND64, ND1000 decoded: the exact long-exposure shutter time behind any filter strength — with a countdown-ready seconds output.

GN = distance × f-number: solve any corner of the flash triangle — reach at an aperture, aperture at a distance — with ISO and zoom scaling.

The shutter that freezes a sprinter, a car or a hummingbird — pixel-level motion math from subject speed, distance and focal length.

Event duration, shooting interval and playback fps solved into frames, clip length and storage — with interval presets for clouds, stars, crowds and construction.

The longest exposure before stars streak — the 500 rule, the stricter NPF reality, and the declination fine print, per lens and sensor.

Temperature + humidity → the NWS heat index, with the caution/danger bands and why 95°F at 70% humidity is a 124°F day for your body.

Canada's muggy-weather number: temperature + dew point → humidex, with the comfort bands Environment Canada actually uses.

The NWS/Environment Canada wind-chill formula with frostbite-time bands — what moving air really does to exposed skin at any temperature.

Magnus-formula dew point from any T/RH pair — the absolute-mugginess number meteorologists trust over relative humidity, with comfort bands.

METAR gives you temperature and dew point — this gives you the RH: Magnus vapor-pressure ratio, plus what happens to RH as the day heats up.

One tool, the whole 'apparent temperature' logic: heat index when hot, wind chill when cold, plain temperature between — exactly how weather apps decide.

The glider pilot's rule made exact: cumulus base ≈ spread × 400 ft — estimate convective cloud base from surface temperature and dew point.

An inch of rain on your roof is hundreds of gallons: rainfall depth × catchment area → litres and gallons, with the runoff coefficient honesty factor.

Every wind unit on one page — with the Beaufort force, its sea-state name, and why aviation, sailing and science each picked a different one.

Every barometric unit translated — hectopascals, inches and millimetres of mercury, psi, atmospheres — with altimeter-setting and weather-map context.

Compare any two tire sizes: diameter, sidewall, circumference and the speedometer error a swap creates — with the ±3% fitment verdict.

What your speedometer really reads after a tire size change — true speed at any indicated speed, the odometer drift, and the ticket-risk direction.

Turn 285/75R16 into '33-inch' truck-speak and back: overall diameter, section width and the flotation-size equivalent of any metric tire.

Revs per mile and per kilometre from any tire size — the number speedometer calibrators, gear charts and drivetrain engineers actually use.

The classic 336 formula: gear ratio × final drive × tire diameter → engine RPM at any speed, plus mph-per-1000-RPM for every cruising argument.

Fit 35s, lose your gearing: the axle ratio that restores factory feel after a tire size change — with the nearest real ring-and-pinion options.

Is your engine loafing, lugging or buzzing at highway speed? Cruise RPM from your gearing — judged against the band your engine type actually likes.

HP = torque × RPM ÷ 5252 — convert either way at any RPM, with kW, PS and Nm, and the reason every dyno chart crosses at 5252.

Your quarter-mile trap speed is a power meter: weight × (MPH/234)³ estimates flywheel horsepower better than any bench-racing claim.

Predict your 1/4-mile ET and trap speed from horsepower and weight — Fox's formulas, the power-to-weight ladder, and an honest traction caveat.

US MPG, UK MPG, L/100km and km/L on one page — converted exactly, with the gallon trap and the reciprocal illusion explained.

Odometer miles ÷ gallons at the pump: your car's true fuel economy by the full-tank method, with cost per mile and the trip-computer reality check.

Electricity price × EV efficiency vs pump price × MPG: the honest per-mile duel, annual savings, and the break-even electricity price.

Bore, stroke and cylinder count → cc, litres and cubic inches — plus bore/stroke ratio and what over-boring or stroking actually buys.

Reaction distance + v²/2μg braking distance for dry, wet, snow and ice — why doubling speed quadruples the stop, in feet and metres.

λ to air-fuel ratio and back across fuels — why 0.85 lambda means 12.5:1 on gasoline but 8.3:1 on E85, and the tuning targets that travel between them.

The displacement-hull speed limit: 1.34 × √LWL — why your boat stops accelerating, with the wave physics that builds the wall.

Hull speed from waterline metres: 2.43 × √LWL(m) — the same wave wall in the units most of the world's boats are documented in.

Paddle-craft speed limits: hull speed for kayaks and canoes, what a paddler's half-horsepower actually achieves against it, and why longer boats win races.

Horsepower to drive a displacement hull near its limit — Gerr's lb-per-hp curves turned into a planning tool, with the brutal last-knot price list.

Past the wall: Crouch's planing formula for speed from power and weight — with the hull-constant table for runabouts, cruisers and racers.

Read any boat's speed from its wake: wavelength of the transverse wave system at a given speed — or speed from an observed wavelength.

The D/L ratio that classifies every hull from ultralight flyer to heavy cruiser — computed, banded and explained.

Estimate a hull's displacement from LWL, beam and draft via the block-coefficient method — the naval architect's first-pass weight check.

Ted Brewer's tongue-in-cheek-turned-canonical comfort ratio: how corky or steady a boat feels in a seaway, from displacement, length and beam.

The post-Fastnet capsize screen: beam against displacement's cube root, with the 2.0 offshore line — what it screens, and what it can't see.

Time your boat's roll, get her metacentric height: the rolling-period test ship's officers use, scaled from tankers to trawlers.

GM built from its parts — KB + BM − KG — with the waterplane-inertia estimate for BM: the naval architecture taught in one calculator.

The stability thief in your tanks: how much GM a slack tank's sloshing liquid destroys — width cubed, as every capsize inquiry rediscovers.

How far she'll lean: heel angle from a weight moved or loaded off-center — the GM-based list formula behind crane lifts, crowd shifts and cargo stows.

How much rode to pay out: scope ratio × (depth + bow height), with tide rise included — the arithmetic behind every quiet night at anchor.

The circle your boat owns at anchor: swing radius from rode, depth and boat length — for spacing in a crowded anchorage and setting the alarm honestly.

What the sag is worth: the wind speed at which your chain's catenary pulls straight and stops protecting the anchor — weight, depth and load in one curve.

Boat windage vs anchor holding: the wind speed your ground tackle is good for, by anchor type, size and bottom — with the squared-wind honesty.

Chain and nylon sized to the load: working loads with safety factors for your boat's storm-design pull, plus the weight-aboard ledger all-chain costs.

The spring in the system: snubber length and diameter for your boat — sized for stretch (the actual job), not just strength.

Weight ↔ displaced volume in salt or fresh water: the principle that floats everything, with the per-inch-of-immersion figure boat loaders need.

How much foam keeps a swamped boat afloat: net buoyancy per cubic foot, the submerged-weight ledger by material, and the level-flotation logic.

The persons-capacity formula behind the placard: length × beam ÷ 15, plus the weight version — and why the rule collapses in chop.

Inches of freeboard per pound of gear: your boat's pounds-per-inch immersion from waterline dimensions — the TPI of ships, scaled to your hull.

Tide height at any hour between tables: the 1-2-3-3-2-1 rule computed exactly, with the sine-curve truth it approximates.

Charted depth + tide height − draft − safety margin: the under-keel arithmetic, with chart-datum logic explained so the sounding makes sense.

Will the mast fit: charted bridge clearance vs your air draft at the actual tide — with the inverted datum logic that trips sailors the wrong way.

Where in the spring-neap cycle are you: range multipliers from days since full/new moon, and what springs vs neaps mean for depth, current and mud.

The E6B's bread and butter: solve time from distance and ground speed — with the answer in decimal hours, minutes, and hh:mm for the navlog.

Leg time computed from TAS and the wind component — out, back, and the round trip that's always slower than calm air.

Airborne time plus taxi, run-up and pattern — the block time that schedules, rentals and airline stats actually run on.

The professional's mental gear: convert any speed to nautical miles per minute and back, with the timing anchors that make cockpit math instant.

Departure time plus legs, with time-zone shift handled — the ETA arithmetic that ATC strips, flight plans and waiting families all depend on.

Three legs with their own ground speeds, plus fuel stops — total airborne time, total trip time and the average speed the whole journey really made.

Invert the time equation: given the miles and the deadline — a slot, sunset, a void time — the ground speed you'd need, and whether it's plausible.

Flight time × fuel flow with reserves on top — the basic fuel equation, with VFR/IFR reserve presets and the gallons↔pounds conversion built in.

Usable fuel into hours aloft and miles covered — with the reserve subtracted first, because endurance to dry tanks is a number for accident reports.

Gallons, litres, pounds and kilograms for avgas and Jet-A — with the density assumptions visible, because the fueler and the load sheet speak different languages.

Aviation's fuel economy: nautical miles per gallon from TAS, wind and flow — compare power settings and altitudes the way the cruise tables wish you would.

Build a calibrated dipstick table for any tank: known additions in, stick markings out — the cheap instrument that outperforms your fuel gauges.

Compute the fuel quantity at which you must divert: alternate distance, flow and reserve in — the gauge (and clock) number that makes the decision before stress does.

What the trip costs in fuel: burn × price, per-person and per-mile splits, and the honest comparison against driving the same journey.

Price the climb's gluttony and the descent's frugality separately — the segment fuel budget that flat cruise-only planning silently misses.

The complete wind triangle solved exactly: course, TAS and wind in — heading, wind correction angle and ground speed out, E6B-style.

One navlog row, fully computed: wind triangle plus variation, leg time and fuel — the four columns of paper planning in a single pass.

The pro's shortcut: max drift = wind ÷ TAS-in-miles-per-minute, scaled by the clock code — mental wind correction within a degree of the exact triangle.

Invert the triangle: heading flown, track made and GPS ground speed in — the actual wind aloft out. Your aircraft is the wind probe.

Split any forecast wind over your course into the headwind that costs time and the crosswind that demands crab — the two numbers every leg brief needs.

Weather ahead, divert now: bearing and distance to the alternate plus today's wind become heading, ETE and fuel — the 60-second cockpit drill, computed.

Apply variation in either direction with the sign handled for you — east is least, west is best, and the mistake is never yours again.

True → Variation → Magnetic → Deviation → Compass, every arrow shown — the full chain from chart course to the number you actually steer.

From magnetic heading to painted runway number and back — including why runways get renumbered as the magnetic pole strolls.

Reciprocals without the 180 fumble: the +200−20 / −200+20 mental method, with course-reversal applications from holds to back-courses.

Northerly turning error quantified: the lead or lag for your latitude and target heading — undershoot north, overshoot south, by this many degrees.

Crossing isogonic lines on a long leg: how much the magnetic heading must drift en route while the true course never moves — and when to re-trim the bug.

The bank angle a standard-rate (3°/sec) turn demands at your TAS — exact formula beside the TAS÷10+7 rule every instrument pilot mutters.

How much sky a turn consumes: radius and diameter from speed and rate (or bank) — the canyon-turn and valley-flying number nobody computes until it matters.

Heading change ÷ 3 = seconds: the partial-panel timed turn computed, with half-standard option and the magnetic-compass-error reasoning attached.

Bank angle into g-load and the stall speed it inflates: the 1/cos φ physics behind the 60°-bank-doubles-nothing-but-45%-more-stall warning.

The 45-180 course reversal timed out: outbound leg, the 45° offset, the 180 back — each segment's seconds and the protected-airspace check.

Side-by-side at your TAS: bank, radius, time-around and g for 3°/s versus 1.5°/s — and the speed where procedure design quietly switches.

Direct, parallel or teardrop — enter your heading to the fix and the inbound course, get the AIM-recommended entry with the sector geometry explained.

Outbound timing for a one-minute inbound in wind, plus the triple-drift outbound crab — the two corrections that keep holds from wandering.

What the stack costs: holding flow × EFC time, the bingo check against your reserves, and the per-circuit price of every extra turn.

The altitude-banded maximum holding speeds (200/230/265 kt and ICAO's bands) checked against your speed — with the why behind each ceiling.

How much sky your hold actually sweeps: leg lengths, turn diameters and total footprint from TAS and wind — the FMS map picture, derived by hand.

Distance-defined holds decoded: where the turns happen for DME vs GPS ('along-track') legs, and the leg-time those distances produce at your speed.

When to start down: the 3-to-1 rule with ground-speed-aware descent rate — altitude to lose, miles required, and the VSI target that flies it.

“Cross 30 miles out at 11,000” solved: the descent rate and angle the restriction demands from your present position — and whether it's still flyable.

Descents planned around ears, not geometry: a 300–500 fpm cabin experience from cruise — when to start, how shallow, and the kids-asleep version.

The miles slowing down steals: TOD computed with the level deceleration segment the basic 3-to-1 forgets — cruise speed to approach speed, honestly.

Heights along a 3° (or any) glidepath: altitude at each distance, the 300-ft-per-mile check, and VSI for your approach ground speed.

How fast can you get down: emergency-descent profiles compared — the time and distance from altitude to breathable air or VMC, configuration by configuration.

How far the glide reaches: altitude AGL times glide ratio, with the POH-figure conversion and the always-too-optimistic warning attached.

The glide that wind bends: range up- and downwind from the same height, with the speed-to-fly adjustment that recovers part of the headwind loss.

Engine failure after takeoff: the altitude a turnback to the runway actually requires — turn geometry, sink in the bank, and the headwind-becomes-tailwind kicker.

Pick cruise altitude by glide footprint: the reachable circle at each altitude, terrain-clearance subtraction, and the gaps where no airport is reachable.

Derive your real glide ratio from the POH chart's numbers — or from your own timed descent — and see how it degrades with speed-discipline errors.

Shoreline-to-shoreline honesty: the altitude a water crossing needs for continuous glide coverage, the wet footprint that remains, and where the point of commitment sits.

The fuel-based PNR: how far out you can fly and still return to departure with reserves — the radius of action that wind shrinks in both directions.

The mid-route line where continuing and turning back take the same time — wind-shifted toward the upwind end, with the time-to-either-option readout.

PNR's stricter sibling: the last point from which returning lands you home WITH full reserves — including the holding/approach allowance the bare formula skips.

The continuous version of PNR thinking: at any checkpoint, fuel-used vs distance-made against plan — the drift that predicts a problem hours before the gauge does.

No-alternate-nearby planning: the fuel a remote destination demands when the nearest divert is far — island rules, computed for any aircraft.

Compute density altitude from field elevation, altimeter setting and temperature — the single number that tells you how your aircraft will really perform today.

Compute humidity-corrected density altitude straight from METAR numbers — QNH, temperature and dew point — using the virtual-temperature method.

Plan hot-and-high operations: density altitude plus normally-aspirated power loss for mountain strips like Leadville, Telluride and Big Bear.

Check density altitude against your helicopter's IGE and OGE hover ceilings — the rotorcraft version of the go/no-go performance check.

Metric density altitude for drone operators — see how thin air at altitude cuts propeller thrust and hover efficiency for multirotors.

Density altitude for towplane operations — climb-rate degradation on tow and the release-altitude math every towpilot and duty instructor needs on a hot day.

Compare side-by-side how the same density altitude treats a turbocharged engine (full power to critical altitude) and a normally-aspirated one (σ-proportional loss).

Compare density altitude at your planned morning departure against the afternoon peak — and see exactly how many feet the heat of the day costs.

Full-metric density altitude for pilots flying QNH in hectopascals and elevations in metres — ICAO units, no inches of mercury anywhere.

Turn a density altitude into the three numbers pilots actually feel: % engine power, takeoff-roll multiplier and climb-rate fraction — physics-based, sources cited.

One set of inputs, four altitudes out — indicated, pressure, density and approximate true altitude — so the alphabet soup finally makes sense.

Convert field elevation and altimeter setting into pressure altitude — the entry point for every POH performance chart.

ICAO-units pressure altitude: field elevation in metres or feet plus QNH in hectopascals, using the 27 ft / 8.23 m per hPa rule.

See how today's QNH shifts the gap between transition altitude and flight levels — and which low flight levels are unusable.

From cruise altitude and your pressurization system's max differential, compute cabin altitude — the pressure altitude your body actually lives at.

Convert a raw station/absolute pressure reading (hPa or inHg) directly into pressure altitude with the exact ISA barometric inversion — no QNH needed.

Pressure altitude planning for the world's high airports — La Paz, Lhasa, Quito, Leadville — where the field starts above many aircraft ceilings.

ICAO cold-temperature corrections: how many feet to add to published approach altitudes when the air is colder than ISA.

Dial in the wrong altimeter setting and every altitude you fly is wrong by a fixed amount — compute exactly how much and in which direction.

The three dimensionless ratios engineers live on — pressure δ, density σ and temperature θ — at any pressure altitude, with optional non-standard temperature.

Enter your cabin pressure altitude and planned time — get the FAA Part 91 oxygen requirements for crew and passengers, decided correctly.

Resolve any reported wind into crosswind and headwind/tailwind components for your runway — with the side of the crosswind called out.

Compute crosswind and headwind twice — at the steady wind and at the gust — plus the gust increment for your approach-speed additive.

Compare today's crosswind component against your aircraft's demonstrated value and your own personal limit — with the verdict spelled out.

Enter the wind once and two runway options — get all four components side by side and the better runway called.

Solo-endorsement crosswind check: today's component against the wind limits your instructor wrote in your logbook, with conservative margins built in.

Crosswind components with tailwheel-specific thresholds — where the groundloop window opens and why the rollout is the real test.

Crosswind and tailwind components against typical transport-category limits — dry vs wet vs contaminated runway, autoland caps included.

Wind components natively in metres per second for glider pilots, microlights and anyone whose ATIS speaks m/s — with the kt conversion alongside.

Learn the 15-30-45-60 clock rule for estimating crosswind in your head — and see exactly how far the shortcut drifts from the exact sine.

Compare measured wind against your drone's rated wind resistance — with gust handling and the altitude wind-gradient trap accounted for.

Scale your sea-level POH takeoff roll to today's density altitude with the physics-based 1/σ² law for normally-aspirated aircraft.

C172S-style takeoff estimate from pressure altitude, temperature and weight — the trainer everyone flies, with the corrections everyone forgets.

Apply the POH wind rules — credit for headwind, penalty for tailwind — and see why a 5-knot tailwind costs more than a 15-knot headwind saves.

Surface factors for turf, long grass, soft ground and snow applied to your paved-runway book figure — the corrections POHs whisper and bush pilots shout.

Price an uphill takeoff in feet — the ~10%-per-1%-gradient planning rule, plus the uphill-takeoff vs downhill-tailwind comparison every one-way strip demands.

Split total takeoff distance into ground roll and air segment, and check a real obstacle at a real distance — not just the chart's standard 50-footer.

The W² law in action: see how each passenger, bag and gallon stretches the takeoff roll — and what off-loading buys back.

Apply the recommended 1.33 safety factor to your computed takeoff distance and test it against TORA — the last gate before the chocks come out.

One chain, every correction: density altitude, weight, wind, surface, slope and safety factor — the full takeoff performance computation in a single pass.

Set your abort gate before the roll: the 50/70 rule's checkpoint speed and distance, computed for your numbers and today's runway.

Quantify what disciplined short-field technique is worth — and what each common sloppy habit costs — against your book numbers.

Scale book landing figures to today's density altitude — a gentler 1/σ law than takeoff, but one that still bites at mountain strips.

Skyhawk landing figures from pressure altitude and temperature — anchored to the published C172S short-field data with the headwind/tailwind notes built in.

The V² tax on 'a few extra knots': how each knot above Vref inflates float and landing distance — the most preventable overrun cause, computed.

Ground-speed-squared honesty about tailwind landings: the per-knot price, the 10-kt certification edge, and the downhill-runway combination that fills accident reports.

AC 91-79 surface factors for wet, standing water, slush, snow and ice — applied to your dry-runway figure, with hydroplaning speed alongside.

Turf landing corrections with the twist nobody expects: dry grass lengthens the roll, but the right technique on firm turf barely notices — wet grass is the real trap.

The dispatch math airlines live by: land within 60% of available runway (×1.67 factor), 1.92 when wet — applied to your numbers, with the Part 91 contrast explained.

Downhill landings stretch the roll ~10% per 1% of grade — compute it, compare against the uphill-landing-with-tailwind alternative, and settle the one-way strip question.

The full landing chain in one pass: density altitude, wind, speed discipline, surface, slope and the 1.43 safety factor — your real number against the real runway.

Pick the runway point past which a touchdown means an overrun — your pre-briefed go-around gate, computed from roll, runway and margin.

Convert calibrated airspeed to true airspeed from pressure altitude and temperature — the E6B classic, exact and instant.

The mental-math TAS rule — add 2% per 1,000 ft — run side-by-side against the exact density calculation so you learn exactly when to trust it.

The exact computation behind the E6B's TAS window — line up pressure altitude against temperature, read true airspeed — with every intermediate value shown.

Measure your aircraft's actual TAS with nothing but GPS ground speeds on four cardinal headings — and get the wind vector as a bonus.

Out against the wind, back with it — compute both ground speeds and the round-trip average that proves a headwind is never repaid by its tailwind.

Same altitude, same indicated speed, different day: see exactly how many knots of true airspeed a temperature swing adds or removes.

TAS for the km/h world — microlights, gliders and European ultralights — with metric altitude and the same exact ISA math underneath.

From POH cruise CAS, altitude, temperature and forecast wind: TAS, ground speed each way, and the altitude where this power setting earns its keep.

The speed chain jets actually use: CAS → EAS (compressibility correction) → TAS, with the error of skipping EAS quantified at your speed and altitude.

Clock a known distance, get your real ground speed and — with the wind backed out — your real TAS: the pre-GPS technique that still audits every instrument.

TAS and temperature in, Mach number out — with the local speed of sound shown, because Mach is a ratio to the air you're actually in.

Convert a cruise Mach to true airspeed at any flight level — using ISA temperature or the actual OAT — the dispatcher's everyday arithmetic.

Mach 1 in knots, km/h, mph and m/s at any altitude — troposphere and stratosphere handled correctly, with the −2.4 kt-per-1,000-ft rule shown.

Where does 280 knots become Mach 0.74? Compute the exact crossover altitude for any climb speed schedule with the real pitot equations.

What Mach does a given calibrated airspeed produce at altitude? The exact subsonic pitot inversion every air-data computer performs.

Total vs static air temperature: compute the ram rise your temperature probe feels at speed, and recover true OAT from an uncorrected gauge.

M0.76 or M0.80? Compute minutes saved on your leg against the steep fuel-burn slope near MMO — the cost-index decision in raw form.

Mach 2 at FL600: TAS, ground-referenced crossing times, and the stagnation heating that set Concorde's skin temperature — supersonic flight in numbers.

Any Mach number to knots, km/h, mph and m/s at your chosen altitude or temperature — because 'Mach 2 in mph' has no answer without the air.

Use sound's travel time to measure distance — lightning flashes, an airshow jet's delayed roar — with the speed of sound corrected for today's temperature.

Universal four-station weight & balance: enter your aircraft's empty weight/arm, loading and limits — get total weight, CG and an in/out-of-envelope verdict.

Skyhawk-specific W&B with the real station arms and the sloped forward limit modeled — enter your tail number's empty weight and load the seats.

PA-28 family W&B with the low-wing's station geometry — front 80.5, rear 118.1, fuel 95, baggage 142.8 — and the sloped forward limit handled.

Two-seat trainer W&B where every pound is visible: the 150/152's tight useful load, side-by-side seating, and the full-fuel-two-adults problem solved honestly.

The POH table method, digitized: weights in, moments/1000 out for every station, summed and divided — matching the paper workflow your examiner expects.

Takeoff legal, landing illegal? Compute the CG at takeoff, at landing and at zero fuel in one pass — the three points the envelope must contain.

The checkride classic solved both ways: how far the CG moves when you shift a weight — or how much weight to shift to hit a target CG.

Convert CG between inches-aft-of-datum and percent of mean aerodynamic chord — the dialect transport aircraft, jets and aerodynamicists speak.

The numbers that sell airplanes, computed honestly: useful load, full-fuel payload, and the fuel/passenger trade — for any aircraft from two placard values.

How much can the baggage bay really take today? The lesser of the structural placard, the gross-weight gap and the aft-CG headroom — computed, not guessed.

Convert climb rate and ground speed into the gradient obstacle charts speak — feet per nautical mile, percent and degrees, all consistent.

A departure says 'minimum 350 ft/nm': enter it with your ground speed and get the VSI number you must beat — the AIM 5-2-9 table as a calculator.

All four gradient dialects interconverted from any one — aviation's ft/nm, engineering's percent, trigonometry's degrees and the metric world's m/km.

Real terrain, real numbers: from runway end to an obstacle's height and distance, the gradient required — compared against the 200 ft/nm standard and your aircraft.

The multiengine truth-teller: OEI climb rate at today's density altitude converted to gradient, against terrain — where 'positive rate' meets 'positive enough.'

Book climb rate withers with density altitude while true airspeed grows — the gradient gets squeezed from both ends. Compute today's real slope.

Same airplane, same VSI — different mountain clearance: how head- and tailwind reshape your gradient over the ground, with the break-even tailwind computed.

Best angle or best rate? Compare gradient, time-to-altitude and position-at-altitude for both speeds — and see exactly what each choice buys and spends.

The POH climb-table computation live: minutes, gallons and miles from origin altitude to cruise altitude, with the average-rate method the tables use.

From two climb-rate data points, derive your aircraft's service ceiling, absolute ceiling and the full rate-vs-altitude line — the linear model inverted.

Standard atmosphere temperature at any altitude — the 15 °C / −2 °C-per-thousand reference every deviation, chart and forecast is measured against.

OAT and altitude in, ISA± out — the deviation that indexes every cruise chart, drives density altitude and prices your climb performance.

The complete standard-atmosphere row for any altitude: temperature, pressure, density, speed of sound and the δ/σ/θ ratios — troposphere and stratosphere both.

Which layer is that altitude in, how far to the tropopause, and what the real tropopause does by latitude and season — the atmosphere's geography lesson.

Two levels of a sounding in, the actual lapse rate out — compared with the dry and moist adiabats to read the atmosphere's stability like a forecaster.

The standard atmosphere in SI: temperature, pressure and density at any altitude in metres — for meteorologists, engineers and the metric flying world.

Translate both ways between actual OAT at a flight level and the ISA± shorthand of forecasts, POH columns and turbine charts — instantly, at any altitude.

From surface temperature and a lapse rate, the altitude where 0 °C lives — the first guess every icing and precipitation-type question starts from.

Standard pressure at any altitude in hPa, inHg, psi and mmHg — with the percentage of sea level that explains ears, chip bags and turbo controllers alike.

ρ in kg/m³ and slugs/ft³ from altitude and actual temperature — the raw quantity beneath lift, drag, engine power and drone thrust.