Triangle Calculator

Solve a flat triangle when you know all three side lengths. This side-side-side tool reports area, perimeter, and the three interior angles; it does not accept angle inputs.

Enter your values in the calculator fields to get an instant result.

Calculator guide

Solve a flat triangle when you know all three side lengths. This side-side-side tool reports area, perimeter, and the three interior angles; it does not accept angle inputs.

Formula or method

Semiperimeter s = (a + b + c) ÷ 2; area = √[s(s − a)(s − b)(s − c)]. The implementation uses an algebraically equivalent rearrangement of Heron’s formula to reduce cancellation. The angle opposite a is arccos[(b² + c² − a²) ÷ (2bc)] × 180/π; repeat for the other sides. Perimeter = a + b + c.

How to use this calculator

  1. Enter Side A, Side B, and Side C in the same length unit, each from 0.000001 to 1,000,000,000. The default sides are 3, 4, and 5.
  2. The two shortest sides must add to more than the longest side; equality describes a line, not a triangle.
  3. Read Area in square units and Perimeter in your input unit. Angles are degrees, ordered opposite the shortest through longest side, not in input-field order.

Worked example

For sides 3, 4, and 5, s = 6 and area = √(6 × 3 × 2 × 1) = 6 square units. Perimeter = 12 units; angles opposite sides 3, 4, and 5 are about 36.87°, 53.13°, and 90°. Sides 13, 14, and 15 give s = 21 and area = √(21 × 8 × 7 × 6) = 84 square units.

Understanding the result

If the inputs are meters, area is square meters and perimeter is meters. Doubling every side multiplies area by four but does not change the angles. Reordering the fields does not change the output order.

Limitations and assumptions

  • Only three-side Euclidean triangles are supported; no SAS, ASA, SSA, height inputs, spherical triangles, diagrams, or unit conversion.
  • Area and perimeter show at most four fractional digits and angles at most two. Small nonzero values use scientific notation. Rounded angles may not add to exactly 180°.
  • Very thin triangles can exceed floating-point precision even within the stated side range; an explicit precision error replaces collapsed or undefined results.

Frequently asked questions

Can I mix feet and inches?

No. Convert all three lengths to the same unit before entering them.

Which angle belongs to Side A?

The output is sorted by opposite side length, not by A/B/C. Match Side A’s length with the shortest, middle, or longest side. Equal sides have equal angles.

Why are 1, 2, and 3 rejected?

The two shorter sides sum to the third, producing zero area rather than a triangle.

Sources

Mathematical calculation only; measured dimensions and rounding affect practical accuracy.