How to use the triangle calculator
- Measure sides a, b and c in the same unit and enter only the numbers.
- Check that every length is positive. A valid triangle also needs any two sides to total more than the remaining side.
- Select Calculate triangle to get area, perimeter, angles A–C and the altitude to each corresponding side.
- Editing any side clears the confirmed result and disables copying until you calculate again.
SSS formulas used
The perimeter is P = a + b + c. With semiperimeter s = P/2, Heron’s formula gives area K = √(s(s−a)(s−b)(s−c)).
The law of cosines gives A = arccos((b²+c²−a²)/(2bc)), with the other angles found cyclically. The three angles total 180°.
Each altitude comes from K = base × height / 2, so hₐ = 2K/a, hᵦ = 2K/b and h𝒸 = 2K/c. Calculations retain internal precision; ordinary displays use at most two decimals.
Worked examples
3–4–5 right triangle
For a=3, b=4 and c=5, the perimeter is 12, area is 6, angles are about 36.87°, 53.13° and 90°, and the three heights are 4, 3 and 2.4.
Equilateral triangle with side 6
All angles are 60°. The perimeter is 18, area is 9√3 ≈ 15.59, and every altitude is 3√3 ≈ 5.2.
Limits and input rules
- This is an SSS solver only; it does not accept SSA, SAS, coordinates or bearings.
- Equal sums create a degenerate straight line and are rejected, as are lengths that cannot satisfy the triangle inequality.
- All sides must share one unit. The calculator does not convert mixed units or infer measurement precision.
- Very small or large meaningful results use scientific notation instead of being shown as a false zero.
Frequently asked questions
Which angle is A?
Angle A is opposite side a; B is opposite b and C is opposite c.
Why was 1, 2, 3 rejected?
Because 1 + 2 equals 3, the points form a straight line and enclose no area.
Does the largest side have the largest angle?
Yes. In any valid triangle, side and opposite-angle order match.