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Pythagorean theorem

Find a missing side in a right triangle. Choose whether the missing side is the longest hypotenuse or one of the two perpendicular legs.

Start with your own numbers

Editable example

An example is filled in. Replace it with your own data to calculate.

abc

For right triangles only. Choose the longest side (hypotenuse) or the other leg.

Choose side to find. Check the selected option before entering the remaining values.
Enter known side a or hypotenuse c, for example 3. Use the displayed unit; replace the example with your own value.
Enter known side b or other leg, for example 4. Use the displayed unit; replace the example with your own value.

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Example result

Length of hypotenuse c

5same unit as input

Known sides must use the same unit. The hypotenuse must be longer than either leg.

Worked steps

  1. c＝√(a² ＋ b²)
  2. ＝√(3² ＋ 4²)
  3. ＝5

For right triangles only. Both inputs must use the same length unit. The hypotenuse must be longer than either leg.

Method and scope

For legs a and b, hypotenuse c is the square root of a squared plus b squared. For a known hypotenuse and one leg, the missing leg is the square root of hypotenuse squared minus known-leg squared.

All side lengths must use the same unit, and the result uses that unit. The hypotenuse is opposite the right angle and must be longer than either leg.

This relationship applies only to a right triangle. A hypotenuse no longer than the entered leg is invalid; rounded measurements can also affect a practical fit.

What this helps you do

Find a missing side in a right triangle. Choose whether the missing side is the longest hypotenuse or one of the two perpendicular legs.

What to enter

Start with side to find, then fill the other relevant fields in the units shown. The field hints explain the required format and examples.

How the calculation works

For legs a and b, hypotenuse c is the square root of a squared plus b squared. For a known hypotenuse and one leg, the missing leg is the square root of hypotenuse squared minus known-leg squared.

Worked example

Legs of 6 and 8 give a hypotenuse of 10. In missing-leg mode, enter hypotenuse 10 in the first side field and known leg 6 in the second to obtain 8.

Understanding the answer

All side lengths must use the same unit, and the result uses that unit. The hypotenuse is opposite the right angle and must be longer than either leg.

Scope and limitations

This relationship applies only to a right triangle. A hypotenuse no longer than the entered leg is invalid; rounded measurements can also affect a practical fit.

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