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Pythagorean Theorem Calculator: Find the Missing Side

This free Pythagorean theorem calculator finds the missing side of a right triangle from the other two. It also gives the area, perimeter and both acute angles.

By Debmedia Technologies LLP · Kolkata, India · Updated

What Is It and When Do You Need It?

The Pythagorean theorem links the three sides of a right triangle. If you know two sides you can find the third, which helps with ladders, ramps, screens, roof pitches and diagonals of rooms.

Fill in two sides and leave one empty. The tool also works out the area, the perimeter and the two other angles.

How to Use This Tool

  1. Type any two of the sides a, b and c.
  2. Leave the unknown one empty.
  3. Press Calculate.
  4. Read the missing side, the angles, the area and the perimeter.

How the Calculation Works

The rule is a² + b² = c², with c as the hypotenuse. To find c, take √(a² + b²). To find a leg, take √(c² − the other leg²). The angles come from the arctangent: angle A = atan(a ÷ b), and angle B = 90° − A.

Worked Example

A ladder reaches 4 m up a wall and its foot is 3 m from the wall, so the ladder is √(16 + 9) = 5 m long. If a 13 m ladder rests with its foot 5 m out, it reaches √(169 − 25) = 12 m high.

Common Uses

  • Checking that a corner is square in building.
  • Finding the diagonal of a screen or room.
  • Ladder, ramp and roof planning.
  • Geometry homework.

Tips and Common Mistakes

  • The hypotenuse is always the longest side.
  • If you fill in a leg longer than c, the numbers cannot form a right triangle.
  • Use the same unit for all sides.

Next, you may need the triangle calculator, distance, midpoint and slope calculator, area calculator, quadratic equation solver.

Everything runs in your browser. Nothing you type is uploaded, stored or sent to any outside service.

Frequently Asked Questions

In a right triangle, the square of the longest side (the hypotenuse) equals the sum of the squares of the other two sides: a² + b² = c².
Fill in any two of the three boxes and leave the third empty. The tool finds the empty one.
A set of three whole numbers that fit the rule, such as 3, 4, 5 or 5, 12, 13 or 8, 15, 17.
Yes. The theorem needs one angle of exactly 90 degrees. For other triangles, use the triangle calculator.

Disclaimer: results are calculated in your browser from the numbers you enter. Check important results before you rely on them for money, health, safety or legal decisions.