Maths / Geometry
Triangle Calculator (Solve SSS, SAS, ASA, AAS, SSA)
Solve a triangle from any three measurements that fix it, three sides, two sides and an angle, or two angles and a side, with every side and angle, the area, the perimeter, the type of triangle, and a drawing to scale. Both answers are shown in the ambiguous SSA case.
Triangle Calculator (Solve SSS, SAS, ASA, AAS, SSA): Three sides or two sides with the angle between them use the law of cosines, c² = a² + b² − 2ab·cos C; two angles and a side use the law of sines, a ÷ sin A = b ÷ sin B = c ÷ sin C, after finding the third angle from the 180° total. Two sides and an angle not between them can fit two triangles: with a = 7, b = 10, and A = 30°, angle B is 45.58° or 134.42°. The area comes from Heron's formula. Runs 100% locally in your browser with zero server file uploads.
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- School & study tools
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- Free · no sign-up
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Runs entirely in your browser
| Sides | a = 3 | b = 4 | c = 5 |
|---|---|---|---|
| Angles | A = 36.8699° | B = 53.1301° | C = 90° |
| Area | 6 | Perimeter | 12 |
A scalene, right-angled triangle; inscribed circle radius 1, circumscribed 2.5.
Sides a, b, and c are opposite angles A, B, and C. The calculator uses the law of cosines, c² = a² + b² − 2ab·cos C, for three sides or two sides and the angle between them, and the law of sines, a ÷ sin A = b ÷ sin B, otherwise. Two sides and an angle not between them can give two triangles, one, or none, and all are shown. The area comes from Heron's formula.
Worked example
A triangle with sides 3, 4, and 5 has angles of 36.87°, 53.13°, and 90°, an area of 6, and a perimeter of 12: the classic right triangle.
For right triangles from two sides, the Pythagorean theorem calculator is quicker.
The ambiguous case
Given a = 7, b = 10, and A = 30°: sin B = 10 × sin 30° ÷ 7 = 0.714, so B is 45.58° or 180° − 45.58° = 134.42°, and both leave room for a third angle. With a = 12, only the first fits; with a = 4, sin B would exceed 1 and there is no triangle.
For trigonometric functions on their own, use the scientific calculator.
How to use it
- Choose what you know.
- Enter the sides and angles, angles in degrees.
- Read the missing sides and angles, the area and perimeter, and check the drawing.
Privacy & limitations
Everything is calculated in your browser.
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Frequently asked questions
Why does SSA sometimes give two answers?
The side opposite the known angle can swing to meet the third side in two places, making an acute and an obtuse version; if it is too short there is no triangle, and if it is long enough there is one.
Why does AAA not work?
Three angles fix the shape but not the size: every scaled copy fits, so at least one side is needed.
Can I solve a right triangle?
Yes: enter 90° as an angle, or use the Pythagorean theorem calculator for two sides.
Free tool · runs in your browser · no account required