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Pythagorean Theorem Calculator
Find a missing right-triangle side with a² + b² = c² and steps.
Quick answer
How do you use the Pythagorean theorem?
Square the two legs, add them, and take the square root to get the hypotenuse: for legs 3 and 4, 9 + 16 = 25 and √25 = 5. To find a leg, subtract: √(13² − 5²) = √144 = 12.
a² + b² = c², so c = √(a² + b²) and a = √(c² − b²). c is the hypotenuse, the side opposite the right angle.
⚡ Answer updates as you type · Enter = calculate · Esc = reset
- Pythagorean theorem: a² + b² = c²
- 3² + 4² = 9 + 16 = 25
- c = √25 = 5 ≈ 5
- Angle opposite a = sin⁻¹(a ÷ c) = 36.8699°; the other acute angle = 90° − 36.8699° = 53.1301°.
Find the missing side of a right triangle with a² + b² = c², including exact radical form, area, perimeter, angles, and steps.
About this Pythagorean Theorem Calculator
The Pythagorean Theorem Calculator finds the missing side of any right triangle using a² + b² = c². Enter two sides and it returns the third in exact simplified radical form and as a decimal, plus the area, perimeter, and both acute angles, with a labeled triangle diagram.
What you'll need
- • Leg a
- • Leg b
- • Hypotenuse c (leave the unknown side blank)
How it works
- 1. Enter any two sides of the right triangle.
- 2. Leave the side you want blank.
- 3. The calculator squares, adds or subtracts, and takes the square root.
- 4. It simplifies the radical and finds angles, area, and perimeter.
- 5. Follow the steps to show your work.
Worked example
A 10 ft ladder leans on a wall with its base 6 ft out. Height reached = √(10² − 6²) = √64 = 8 ft. Legs 5 and 5 give a hypotenuse of √50 = 5√2 ≈ 7.0711.
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Pythagorean Theorem Calculator FAQ
What is the Pythagorean Theorem Calculator?
The Pythagorean Theorem Calculator is a free online tool that helps you find a missing right-triangle side with a² + b² = c² and steps.
How do I use the Pythagorean Theorem Calculator?
Open the Pythagorean Theorem Calculator, enter the requested values, and review the instant estimate on the page.
Is the Pythagorean Theorem Calculator free?
Yes. The Pythagorean Theorem Calculator is free to use on Fast Online Calculator and does not require an account.
Which side is the hypotenuse?
The hypotenuse is the longest side, directly across from the 90° angle. It is always c in a² + b² = c².
Does the Pythagorean theorem work for all triangles?
No, only right triangles. For other triangles use the law of cosines: c² = a² + b² − 2ab·cos(C).
What are Pythagorean triples?
Whole-number side sets that fit a² + b² = c², such as 3-4-5, 5-12-13, 8-15-17, and 7-24-25, plus any multiples like 6-8-10.
How do I write the answer in simplest radical form?
Pull out perfect-square factors: √50 = √(25 × 2) = 5√2. The calculator shows the exact form whenever the answer is not a whole number.
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