Destination Point Calculator (Start + Bearing + Distance)
Where do you end up? Start coordinates, a bearing and a distance → the destination lat/long, by exact great-circle math.
This is dead reckoning's forward problem — the navigator's daily bread for five centuries, now the geometry inside every 'search within radius', drone waypoint plan and artillery solution. Bearings are TRUE; apply magnetic declination before using a compass heading.
Formula
⚠️ Great-circle estimates on a spherical Earth (±0.5% vs ellipsoidal) — for surveying, legal boundaries and navigation use geodetic-grade tools and official datums.
Where do you end up? Start coordinates, a bearing and a distance → the destination lat/long, by exact great-circle math.
About Destination Point Calculator (Start + Bearing + Distance)
Navigation has two classic problems: where am I (the inverse), and where will I be (the direct) — this tool solves the second. Give it a starting position, a true bearing and a distance, and spherical trigonometry projects the destination exactly, in decimal degrees and DMS. It's the math inside drone waypoint generation, marine dead reckoning, search-pattern planning, geocache puzzles and every 'project a point' GIS button — exposed with its formula visible.
How to use Destination Point Calculator (Start + Bearing + Distance)
- 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 φ₂ = asin(sinφ₁·cosδ + cosφ₁·sinδ·cosθ); λ₂ = λ₁ + atan2(sinθ·sinδ·cosφ₁, cosδ − sinφ₁·sinφ₂), δ = d/R substituted step by step.
- 4Adjust inputs (or flip the unit toggle) until the scenario matches yours, then copy or share the result.
Why use Destination Point Calculator (Start + Bearing + Distance)?
- ✓Instant, free and private — every calculation runs in your browser, nothing is uploaded
- ✓Built on the published formula φ₂ = asin(sinφ₁·cosδ + cosφ₁·sinδ·cosθ); λ₂ = λ₁ + atan2(sinθ·sinδ·cosφ₁, cosδ − sinφ₁·sinφ₂), δ = d/R with sources cited on the page
- ✓This is dead reckoning's forward problem — the navigator's daily bread for five centuries, now the geometry inside every 'search within radius', drone waypoint plan and artillery solution. Bearings are TRUE; apply magnetic declination before using a compass heading.
- ✓Switch units, tweak any input and watch every result update live
Frequently asked questions
What real tasks use the destination-point calculation?+
More than navigation: projecting drone survey waypoints from a home point (bearing/range grids), laying out search-and-rescue patterns (expanding squares are sequences of this calculation), estimating a vessel's DR position between GPS fixes, reverse-engineering 'go 2.3 km at 140°' geocache and orienteering clues, plotting radio-direction-finding fixes, and generating points-on-a-circle for coverage rings (run it per bearing). Anywhere a position, direction and distance meet, this is the kernel.
How does accuracy hold up over distance?+
The spherical formula is exact — on a sphere. Against the real WGS-84 ellipsoid it drifts like all spherical work: roughly 0.3–0.5% of distance in the worst orientations, so metre-level over a few km, up to a few km over an ocean. Bearing input error dominates in practice: 1° of bearing error displaces the destination by 1.75% of the distance (sin 1°) — 1.75 km per 100 km — which is why long dead-reckoning legs were always checked against celestial or landmark fixes.
My compass says 65° — can I enter that directly?+
Only after converting to true: this tool (like all geodesic math) works in true bearings referenced to geographic north. Magnetic compasses read true minus local declination — if your declination is 10°E, a compass 65° is a true 75°. Aviation adds device deviation on top (the compass card's own error). The order of operations navigators chant: Compass → Deviation → Magnetic → Variation → True ('Can Dead Men Vote Twice'). Skip it and every result rotates by your local declination.
Why does longitude shift more per kilometre as I go poleward?+
Meridians converge: a degree of longitude spans cos(latitude) × 111.32 km — 111 km at the equator, 78 at 45°, 0 at the pole. The destination formula handles this automatically (the atan2 term), but it explains otherwise-odd outputs: 100 km due east from latitude 60° moves you 1.80° of longitude, the same trip at the equator only 0.90°. Our degree-length calculator tabulates exactly this shrinkage.
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