🔺 Triangle Calculator
Solve any triangle from three values — SSS, SAS, ASA, AAS or the ambiguous SSA case — with angles, area, perimeter, heights, medians and a drawing.
Fill in any three values, including at least one side. Side a is opposite angle A.
| Side | Length | Opposite angle |
|---|---|---|
| a | 5 | A = 43.8979° |
| b | 7 | B = 76.1021° |
| c | 6.245 | C = 60° |
Computed values are in bold. Lengths use whatever unit you entered; area is in that unit squared.
What Triangle Calculator Does
This triangle calculator solves any triangle — not just right triangles. Enter any three of the six measurements (three sides and three angles), including at least one side, and it works out which case you have: three sides (SSS), two sides and the angle between them (SAS), two angles and a side (ASA or AAS), or two sides and an angle that is not between them (SSA).
It returns the missing sides and angles, then the area, perimeter, semiperimeter, all three heights and medians, the inradius and circumradius, and whether the triangle is acute, right or obtuse and scalene, isosceles or equilateral. A drawing to scale shows the shape, and when the SSA case allows two different triangles you can switch between them.
How to Use Triangle Calculator
- Enter any three known values, including at least one side
- Choose degrees or radians for the angles
- Read the missing sides and angles, highlighted in bold
- Check area, perimeter, heights, medians and the radii
- For the SSA case, switch between the two possible triangles
Formula Used by Triangle Calculator
Law of cosines (SSS and SAS)
c² = a² + b² − 2ab·cos C
Worked example
a = 5, b = 7 and the angle between them C = 60°.
- c² = 25 + 49 − 70 × 0.5 = 39
- c = √39 = 6.245
- A = 43.90°, B = 76.10° from the law of sines
Result: Area = ½ × 5 × 7 × sin 60° = 15.16.
Law of sines and the ambiguous case
a ÷ sin A = b ÷ sin B = c ÷ sin C
Worked example
a = 6, b = 8 and A = 35° (SSA).
- sin B = 8 × sin 35° ÷ 6 = 0.765
- B = 49.89° or 180° − 49.89° = 130.11°
- C = 95.11° with c = 10.42, or C = 14.89° with c = 2.69
Result: Two different triangles fit these measurements.
Which Rule to Use
| You know | Case | Start with |
|---|---|---|
| Three sides | SSS | Law of cosines for an angle |
| Two sides and the angle between them | SAS | Law of cosines for the third side |
| Two angles and the side between them | ASA | Third angle = 180° − the other two, then law of sines |
| Two angles and another side | AAS | Same as ASA |
| Two sides and an angle not between them | SSA | Law of sines — check for 0, 1 or 2 triangles |
| Three angles | AAA | Not solvable: the size is unknown |
Heights, Medians and Radii
| Measure | Formula |
|---|---|
| Height to side a | hₐ = 2 × Area ÷ a |
| Median to side a | mₐ = ½√(2b² + 2c² − a²) |
| Inradius (inscribed circle) | r = Area ÷ s, where s = (a + b + c) ÷ 2 |
| Circumradius (circumscribed circle) | R = a ÷ (2 sin A) |
| Area from three sides (Heron) | √(s(s − a)(s − b)(s − c)) |
How to Read Your Result
How many SSA triangles?
With angle A, its opposite side a and another side b: if a is shorter than b·sin A, no triangle exists; if it equals b·sin A, there is one right triangle; if it falls between b·sin A and b, there are two; and if a is at least b, there is one. The calculator checks this and shows every valid answer.
Rounding and precision
The values you enter are used exactly and computed values are rounded only for display. If you copy rounded answers back in as inputs, small differences in the last decimal place are expected.
Right triangles
For a right triangle, the right triangle calculator is quicker: it needs only two values and also lists the trigonometric ratios. This page is for every triangle, including oblique ones with no right angle.
Limitations & Accuracy Notes
- Enter exactly three values; extra values are not checked for consistency.
- Angles must be strictly between 0° and 180° and sides greater than zero; flat (degenerate) triangles are rejected.
- Plane triangles only — spherical triangles, as used in navigation and astronomy, follow different rules.