Law of Sines Calculator

a/sin(A) = b/sin(B) = c/sin(C). Solve any triangle given AAS / ASA / SSA.

Inputs

Result

Loading calculator…
—

General calculation reads

Amazon affiliate
How Not to Be Wrong
Jordan Ellenberg - math thinking
Shop on Amazon
The Joy of X
Steven Strogatz - accessible math
Shop on Amazon
Scientific calculator (Casio fx-991EX)
Shop on Amazon

As an Amazon Associate we may earn from qualifying purchases. This does not add cost for you.

How to use this calculator

  • Enter angle A and its opposite side a.
  • Enter angle B.
  • Read computed angle C and remaining sides.

About this calculator

Law of sines: a/sin(A) = b/sin(B) = c/sin(C) = 2R (where R = circumradius). Use to solve triangles when you know two angles and one side (AAS or ASA): the third angle is 180° − A − B, then ratios give the missing sides. The SSA case ("ambiguous case") can have 0, 1, or 2 valid triangles depending on configuration.

Frequently asked

When does law of sines work?+
Best for AAS, ASA, or SSA triangles (one side + opposite angle, plus one more piece). For SAS or SSS, use law of cosines.
Why does C = 180° − A − B?+
Triangle interior angles sum to 180°. Once you know two, the third follows.
Ambiguous case (SSA)?+
Given two sides + non-included angle, sometimes 0, 1, or 2 solutions exist. This calc takes AAS only.
Why 2R appears?+
The common ratio in law of sines equals the diameter of the circumscribed circle. Useful in extended trigonometry.
Real-world use?+
Surveying (measuring distances using known angles), navigation, and any triangulation problem.

Related calculators

Law of Cosines Calculator
c² = a² + b² − 2ab·cos(C). Solve any triangle given SAS or SSS.
Right Triangle Solver
Given any 2 of (a, b, c, angle), solve all remaining sides + angles.
Unit Circle Calculator
Angle θ → (cos θ, sin θ) coordinates on the unit circle. Reference angle + quadrant.
Pythagorean Theorem Calculator
a² + b² = c². Solve for hypotenuse or missing leg of a right triangle.
Distance Between Two Points (2D + 3D)
d = √(Δx² + Δy² [+ Δz²]). Pythagorean distance in the plane or 3-space.
Triangle Perimeter Calculator
P = a + b + c. Sum of all three sides.

More tools you might like

Hand-picked tools that pair well with this one — same audience, same intent.

Law of Cosines Calculator
Calc

c² = a² + b² − 2ab·cos(C). Solve any triangle given SAS or SSS.

Right Triangle Solver
Calc

Given any 2 of (a, b, c, angle), solve all remaining sides + angles.

Unit Circle Calculator
Calc

Angle θ → (cos θ, sin θ) coordinates on the unit circle. Reference angle + quadrant.

Pythagorean Theorem Calculator
Calc

a² + b² = c². Solve for hypotenuse or missing leg of a right triangle.

Triangle Perimeter Calculator
Calc

P = a + b + c. Sum of all three sides.

Finance Calculator (TVM 5-Key Solver)
Finance

Time-value-of-money solver — solve for Present Value, Future Value, Payment, Periods, or Interest rate given the other four. The HP-12C and TI BA-II Plus core in a free browser tool.