Right Triangle Calculator

Solve any right triangle instantly with step-by-step solutions. Choose from four input modes:

  • Two legs — Enter both legs to find the hypotenuse and all angles
  • Leg + hypotenuse — Enter one leg and the hypotenuse to find the missing leg
  • Leg + angle — Enter one leg and the opposite acute angle to solve the triangle
  • Hypotenuse + angle — Enter the hypotenuse and an acute angle to find both legs

Every calculation includes a visual diagram, all computed values (sides, angles, area, perimeter), and a complete step-by-step solution.

Enter both legs (a and b) to find the hypotenuse and angles

Formulas Used

Pythagorean theorem

Sine ratio

Cosine ratio

Tangent ratio

Area of a right triangle

How to Use This Calculator

  1. Select a mode using the buttons at the top — choose based on which values you already know
  2. Enter your values in the input fields
  3. See the full solution — all missing sides, both acute angles, area, and perimeter appear instantly with step-by-step work

The calculator labels the triangle with standard convention: side a is the vertical leg, side b is the horizontal leg, and side c is the hypotenuse. Angle A is opposite side a, and Angle B is opposite side b. The right angle (90°) is where the two legs meet.

What Is a Right Triangle?

A right triangle has one angle that is exactly 90 degrees. The side opposite the right angle — the longest side — is called the hypotenuse. The other two sides are called legs.

Right triangles are the foundation of trigonometry. Every sine, cosine, and tangent value comes from the ratios of sides in a right triangle.

The Pythagorean Theorem

The relationship between the three sides of a right triangle is:

c2=a2+b2c^2 = a^2 + b^2

where cc is the hypotenuse and aa and bb are the legs. This formula lets you find any side when you know the other two. For a deeper explanation with examples, see The Pythagorean Theorem.

SOH CAH TOA — Finding Sides and Angles

When you know one side and one acute angle, the trig ratios connect them:

sin⁡(A)=oppositehypotenuse=ac\sin(A) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{a}{c}

cos⁡(A)=adjacenthypotenuse=bc\cos(A) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{b}{c}

tan⁡(A)=oppositeadjacent=ab\tan(A) = \frac{\text{opposite}}{\text{adjacent}} = \frac{a}{b}

Learn more about choosing the right ratio in SOH CAH TOA and When to Use Sine, Cosine, or Tangent.

When You’ll Need Right Triangles

Right triangle calculations come up constantly in practical work: