Right Triangle Calculator

Solve missing sides, acute angles, area, and perimeter from any valid pair of right-triangle measurements.

Right triangle solver
Enter exactly two known values to solve the triangle.

Angles A and B are measured in degrees; the third angle is always 90 degrees.

About right triangle calculations

A right triangle contains one 90-degree angle and two acute angles. The side opposite the right angle is the hypotenuse c, which is always the longest side. The other sides, a and b, are called legs. In this calculator, angle A is opposite side a and angle B is opposite side b. Since all triangle angles total 180 degrees, A + B always equals 90 degrees. When two sides are known, the Pythagorean theorem provides the missing side: a² + b² = c². With both legs, calculate c as √(a² + b²). With one leg and the hypotenuse, rearrange the equation and take the square root of the difference. A proposed hypotenuse must be longer than either leg, or no real right triangle can be formed. Trigonometric ratios connect sides and angles. For angle A, sine is a/c, cosine is b/c, and tangent is a/b. Inverse sine, cosine, or tangent finds an angle from known sides. If one side and one acute angle are known, the same ratios can be rearranged to calculate both missing sides. The calculator accepts degrees and reports both acute angles in degrees. Exactly two independent measurements are enough as long as at least one is a side. Two angles alone determine shape but not scale, so infinitely many similar triangles would satisfy them. Two entered sides, or one side plus either acute angle, determine one unique triangle. Inputs must be positive, acute angles must fall between 0 and 90 degrees, and a leg cannot equal or exceed a supplied hypotenuse. Area is half the product of the perpendicular legs, A = ab / 2. Perimeter is the sum a + b + c. Side results use the same unit as the known side, area uses its square, and angles use degrees. Displayed results are rounded to six decimal places after calculations at full floating-point precision. Right-triangle solving is used in surveying, construction, navigation, roof pitch, screen dimensions, ramps, ladders, and coordinate geometry. Before relying on a practical result, confirm that the measured sides are straight, the assumed corner is truly square, and every length uses the same unit. A useful check is that the reported hypotenuse must be longest, both acute angles must add to 90 degrees, and the three sides must satisfy the Pythagorean equation within normal rounding tolerance.

Right triangle examples

Each pair of known values demonstrates a different solving route.

Known valuesSelected resultsMethod
a = 3, b = 4c = 5; A = 36.869898°Use the Pythagorean theorem, then inverse tangent.
a = 5, c = 13b = 12; area = 30Subtract a² from c² before taking the square root.
a = 7, A = 30°b = 12.124356; c = 14Use tangent for b and sine for c.
c = 10, B = 60°a = 5; b = 8.660254Resolve the hypotenuse with cosine and sine.

How to use the right triangle calculator

  1. Identify the hypotenuse and label each leg according to its opposite acute angle.
  2. Enter exactly two known measurements, with at least one side length.
  3. Use degrees for Angle A or Angle B and leave all unknown fields blank.
  4. Select Calculate to solve every remaining side, angle, area, and perimeter.
  5. Check that the hypotenuse is longest and the two acute angles total 90 degrees.

Right triangle calculator FAQ

Which side is the hypotenuse?

The hypotenuse is opposite the 90-degree angle and is the triangle's longest side. It is labeled c in this calculator.

Why do I need at least one side?

Angles determine only a triangle's proportions, not its size. One side establishes scale so every other length can be calculated.

Can either acute angle be entered?

Yes, enter Angle A or Angle B together with one side. The calculator derives the other acute angle because the pair must total 90 degrees.

What happens if a leg is longer than the hypotenuse?

Those values cannot form a right triangle, so the calculator reports an input error. The hypotenuse must be strictly longer than each leg.

How is triangle area calculated?

The two legs are perpendicular and act as base and height. Multiplying them and dividing by two gives the area.