Standard Rate Turn Bank Angle Calculator
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.
Standard rate completes 360° in two minutes — the basis of every timed turn and holding pattern. Past ~170 kt the required bank exceeds 30°, so faster aircraft fly half-standard instead: the rule and the physics both say so.
Formula
⚠️ For flight planning and education only — verify with official sources and certified equipment. Not for primary navigation.
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.
About Standard Rate Turn Bank Angle Calculator
Instrument flying is built around one turn rate — 3° per second, two minutes around — and the bank that produces it grows with speed. This calculator solves the exact relation (tan φ = Vω/g) for any TAS and rate, displays the beloved TAS÷10+7 approximation beside it, and notes the regime change at higher speeds where standard rate would demand banks steep enough that procedure design switches to half-standard.
How to use Standard Rate Turn Bank Angle Calculator
- 1Enter — sensible defaults are pre-filled so you see a worked result immediately.
- 2Read the live results: .
- 3Check the "With your numbers" line to see the formula tan(φ) = V·ω/g; rule of thumb: bank ≈ TAS/10 + 7 (for 3°/s) substituted step by step.
- 4Adjust inputs (or flip the unit toggle) until the scenario matches yours, then copy or share the result.
Why use Standard Rate Turn Bank Angle Calculator?
- ✓Instant, free and private — every calculation runs in your browser, nothing is uploaded
- ✓Built on the published formula tan(φ) = V·ω/g; rule of thumb: bank ≈ TAS/10 + 7 (for 3°/s) with sources cited on the page
- ✓Standard rate completes 360° in two minutes — the basis of every timed turn and holding pattern. Past ~170 kt the required bank exceeds 30°, so faster aircraft fly half-standard instead: the rule and the physics both say so.
- ✓Switch units, tweak any input and watch every result update live
Frequently asked questions
Why is the rule TAS over ten plus seven?+
It's a linearization of the arctangent around GA speeds: at 100 kt the exact bank is 16.7° (rule: 17), at 140 kt 22.4° (rule: 21). Within ±1.5° from 80 to 180 knots — tighter than anyone holds bank in turbulence. Beyond that range the tangent's curvature defeats the straight line, conveniently right where half-standard takes over anyway.
Where does the 3°-per-second standard come from?+
The two-minute turn predates gyros' precision era: a full circle in 120 seconds proved a comfortable instrument-flying compromise — brisk enough for procedures, gentle enough for partial panel and passenger comfort — and got institutionalized in turn-indicator markings, holding pattern design and timed-turn technique. Turn coordinators mark it as the 'doghouse' or index marks.
Why do jets fly half-standard or bank-limited turns?+
At 250 kt, standard rate demands 34° of bank — above the 30° passenger-comfort and autopilot ceiling, and uncomfortably near buffet margins high and heavy. Procedure design (TERPS/PANS-OPS) therefore assumes the lesser of 3°/s or a fixed bank (commonly 25°), and jet autopilots cap bank accordingly. Holding entries at FL350 are wide, slow arcs for exactly this reason.
Turn coordinator or attitude indicator — which flies the rate?+
The turn coordinator displays rate directly (wing on the index = standard rate) and is the primary instrument for it — bank is just the means. The discipline: roll to the rule-of-thumb bank on the AI, then trim the rate against the TC's index. When the AI dies (the classic partial-panel scenario), the TC alone flies every turn — at, naturally, standard rate and timed.
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