Triangulation Calculator — Locate a Target from Two Angles
Enter the baseline distance between two observation points and the angles each observer measures to a common target. The calculator uses the law of sines to find the distance from each point to the target and plots the triangle.
units
°
°
AT = D · sin(β) / sin(α + β)
- 1
Angle at target
180° − 45° − 60° = 75The three interior angles of any triangle sum to 180°. - 2
sin(α + β)
sin(45° + 60°) = 0.965926 - 3
Distance A → Target
100 × sin(60°) ÷ 0.965926 = 89.658
How does this calculator work?
Given baseline D and angles α (at A) and β (at B): AT = D·sin β/sin(α+β), BT = D·sin α/sin(α+β), angle at target = 180°−α−β. The target coordinates are (AT·cos α, AT·sin α) relative to A. All computed from the law of sines — no iteration needed.
Formula
How this is calculated
Triangulation locates an unknown point T by measuring the angle from each end of a known baseline to T. With observer A at the origin and observer B at distance D along the x-axis, angle α is measured at A (from the line AB toward T) and angle β at B (from line BA toward T). The three angles of the resulting triangle must sum to 180°, so the angle at T is 180° − α − β.
Applying the law of sines to triangle ABT: AT / sin β = BT / sin α = D / sin(180° − α − β) = D / sin(α + β)
This gives AT = D · sin β / sin(α + β) and BT = D · sin α / sin(α + β) directly, without needing any trigonometric iteration. The target coordinates (with A at the origin) are Tx = AT · cos α and Ty = AT · sin α.
Triangulation is the basis of surveying, GPS positioning, range-finding and navigation. The accuracy depends on the baseline length relative to the target distance — longer baselines relative to target range give better angle resolution and smaller position error.
Frequently asked questions
Triangulation is fundamental to surveying, GPS satellite positioning, cell-tower phone location, radar and sonar range-finding, photogrammetry and astronomical parallax. By measuring angles from the ends of a known baseline (which might be the distance between two GPS satellites or two base stations) the exact position of an unknown point can be found without physically visiting it.
If α + β equals or exceeds 180°, the angle at T would be zero or negative, meaning no valid triangle can be formed — the target lies on or behind the baseline. The calculator shows a warning in that case. In practice this means the two lines of sight from A and B are parallel or diverge.
This calculator uses interior angles measured from the baseline toward the target. If you have compass bearings (measured clockwise from north), first convert: interior angle at A = |bearing_to_T − bearing_from_A_to_B|, ensuring you pick the supplementary angle if the result exceeds 180°. The geometry is the same; only the coordinate frame differs.
Also known as
TG we-Calculate Editorial Team. (2026). Triangulation Calculator — Locate a Target from Two Angles [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/triangulation-calculator
TG we-Calculate Editorial Team. "Triangulation Calculator — Locate a Target from Two Angles." TG we-Calculate. 2026. https://we-calculate.com/calculator/triangulation-calculator.
TG we-Calculate Editorial Team, "Triangulation Calculator — Locate a Target from Two Angles," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/triangulation-calculator
@misc{wecalculate_triangulation_calculator, title = {Triangulation Calculator — Locate a Target from Two Angles}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/triangulation-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?