Free calculator · Years 8 to 10

Pythagoras calculator, with the working out

Enter any two sides of a right-angled triangle. You’ll get the missing side and every step of the working, set out the way your teacher wants to see it.

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Free to download · 7-day free trial on monthly · Years 7 to 10 maths · On iPhone. Android coming soon

Find a missing side

abc

The hypotenuse is 10 cm

  1. You're finding the hypotenuse cc, the longest side, opposite the right angle.
  2. Write Pythagoras' theorem: a2+b2=c2a^2 + b^2 = c^2
  3. Substitute the two shorter sides: 62+82=c26^2 + 8^2 = c^2
  4. Square each side length: 36+64=c236 + 64 = c^2
  5. Add: c2=100c^2 = 100
  6. Take the square root of both sides:
  7. c=100=10 cmc = \sqrt{100} = 10 \text{ cm}

Fill in any two sides and leave the one you want blank. The hypotenuse is the side opposite the right angle.

How it works

It uses Pythagoras' theorem, a2+b2=c2a^2 + b^2 = c^2, where cc is the hypotenuse.

  • Finding the hypotenuse: c=a2+b2c = \sqrt{a^2 + b^2}
  • Finding a shorter side: a=c2−b2a = \sqrt{c^2 - b^2}

It only works for right-angled triangles. If the question involves an angle, use the trigonometry calculator instead.

Learning the method? Read Pythagoras’ theorem explained, with worked examples and practice questions.

Pythagoras calculator: questions

How do I find the hypotenuse?

Enter the two shorter sides and leave the hypotenuse blank. The calculator squares them, adds them and takes the square root, showing each step.

How do I find a missing shorter side?

Enter the hypotenuse and the side you know, and leave the other blank. It squares the hypotenuse, subtracts the square of the known side and takes the square root.

Why does it say the hypotenuse must be the longest side?

The hypotenuse is opposite the right angle and is always the longest side. If the number you entered as the hypotenuse is shorter than another side, it's probably in the wrong box.

Does it round the answer?

If the answer is a whole number it shows it exactly. Otherwise it shows the exact square root and the answer rounded to 2 decimal places, which is what most questions ask for.

Tuterly · Years 7 to 10 maths

Practise until you don’t need the calculator

Tuterly saves the questions you get wrong, shows the working, and gives fresh questions on the same skill until it’s mastered.

Coming soon on iPhone. Android soon after.

Launch price: 50% off until 31 March 2027. $17.99 $8.99 a week or $59.99 $29.99 a month.

We'll email you when Tuterly launches, plus occasional maths tips and offers. Unsubscribe any time. See our privacy policy.

Free to download · 7-day free trial on monthly · Years 7 to 10 maths · On iPhone. Android coming soon
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