Home·Geometry

Pythagorean Theorem

Square both legs, add them, take the square root. Enter 3 and 4 and you get exactly 5.

Your numbers

Hypotenuse

5cm

Area

6cm²

Angle (°)

36.87°

Formula

Hypotenuse = √(Side a² + Side b²)

The angle shown is the one opposite side a. Only the two legs adjoining the right angle belong in the inputs.

What to enter

InputDefaultAccepted range
Side a (cm)The length of the first side.30 and up
Side b (cm)The length of the second side.40 and up

Step by step

FormulaHypotenuse = √(Side a² + Side b²)
With the default numbersHypotenuse = √(3² + 4²)
AnswerHypotenuse = 5 cm

Quick reference table

Results when only Side a (cm) changes and everything else stays put.

Side a (cm)Hypotenuse (cm)Area (cm²)Angle (°) (°)
1.54.272320.56
2.254.58944.529.36
35636.87
4.56.0208948.37
67.21111256.31

What each result means

ResultAt default values
Hypotenuse (cm)The longest side of a right triangle, facing the right angle.5
Area (cm²)The space a shape covers — length squared.6
Angle (°) (°)An angle in degrees; a full turn is 360°.36.87

Common mistakes

The angle shown is the one opposite side a. Only the two legs adjoining the right angle belong in the inputs.

Glossary

Side a
The length of the first side.
Side b
The length of the second side.
Hypotenuse
The longest side of a right triangle, facing the right angle.
Area
The space a shape covers — length squared.
Angle (°)
An angle in degrees; a full turn is 360°.

Frequently asked questions

Q. How is Pythagorean Theorem calculated?

Hypotenuse = √(Side a² + Side b²) — Square both legs, add them, take the square root. Enter 3 and 4 and you get exactly 5.

Q. Can you walk through an example?

With Side a 3cm, Side b 4cm, the answer is Hypotenuse 5cm.

Q. What do I need to enter?

Enter Side a, Side b. The result recalculates as you type, and an empty box counts as zero.

Q. How much does the answer move if I change a number?

Changing only Side a (cm) moves the answer to Side a (cm) 1.5 → Hypotenuse (cm) 4.272 and Side a (cm) 6 → Hypotenuse (cm) 7.2111. The table below lays out five steps.

Q. How are the numbers rounded?

Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.

Q. Anything to watch out for?

The angle shown is the one opposite side a. Only the two legs adjoining the right angle belong in the inputs.

Related calculators

Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.