JLJosh Liljenquist

Geometry calculator

Right triangle calculator

Solve a right triangle from two known sides or from one side and one acute angle. The result checks impossible combinations, identifies the hypotenuse, and reports both acute angles along with area and perimeter.

By

Sides and anglesArea and perimeterImpossible-input checks

Enter known values

Enter the known values and select Calculate.

How to use this calculator

  1. Enter exactly two known values.
  2. Use c only for the side opposite the 90-degree angle.
  3. An angle entry must be one acute angle between 0° and 90°.
  4. Keep all side values in the same unit; the output preserves that unit generically.

Formula and method

Sides use a² + b² = c², where c is the hypotenuse. Acute angles use tangent or sine ratios. Area = a × b ÷ 2, and perimeter = a + b + c.

Worked example

With legs a = 3 and b = 4, c = 5. Angle A is about 36.87°, angle B is about 53.13°, area is 6 square units, and perimeter is 12 units.

Assumptions and result interpretation

  • The triangle contains one 90-degree angle.
  • Inputs describe the same triangle and side labels follow the diagram convention stated on the page.
  • Displayed decimals are rounded; calculations use unrounded values.
  • The result does not determine construction tolerances or field measurement accuracy.

Understanding the result

Two sides uniquely determine a right triangle. One side and one acute angle also determine it because the other acute angle must complete 90 degrees.

Common mistakes

  • Entering the longest side as a leg
  • Using degrees and radians interchangeably
  • Entering more than two known values that conflict
  • Rounding a missing side before calculating area

Methodology sources

Pythagorean theorem calculatorCylinder volume calculatorStair calculator

Browse all calculators.

Use this result as a calculation aid. Confirm input definitions, required precision, and any governing policy or professional standard separately.