Math
Hypotenuse Calculator
The hypotenuse is the longest side of a right triangle, opposite the right angle.
Enter the two legs, or one leg and an acute angle, and this calculator returns the hypotenuse in exact form and as a decimal, along with the other leg, both angles, and the area.
One side that touches the right angle.
The other side that touches the right angle.
Try an example
Result
Hypotenuse c
—
- Exact form
- —
- Other leg
- —
- Acute angles
- —
- Area
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
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Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the hypotenuse calculator solves
The The longest side of a right triangle, always opposite the right angle. is the side opposite the right angle and always the longest side. With both legs you use the Pythagorean theorem; with one leg and an acute angle you use sine or cosine.
| Legs | Hypotenuse (exact) | Decimal |
|---|---|---|
| 3 and 4 | 5 | 5 |
| 6 and 8 | 10 | 10 |
| 1 and 1 | √2 | 1.4142 |
| 5 and 5 | 5√2 | 7.0711 |
| 2 and 3 | √13 | 3.6056 |
How to use it
- Choose whether you know both legs or a leg and an angle.
- Enter the values. Angles are in degrees.
- Read the hypotenuse in The answer kept as a fraction or radical instead of a rounded decimal. (when it simplifies) and as a decimal.
- Check the other leg and the two acute angles if the problem continues.
How to read the answer
An exact form like 5√2 is the precise answer; the decimal is rounded to four places. The two acute angles always add to 90°. Angle A is opposite leg a.
Common mistakes and edge cases
- Adding the legs and then squaring: (a + b)² is not a² + b².
- Using a leg as the hypotenuse when solving for a missing leg — that page is the Pythagorean theorem calculator with the leg mode.
- Mixing up opposite and adjacent: the angle opposite a leg is across from it; the adjacent angle is formed by that leg and the hypotenuse.
- An angle of exactly 90° or 0° does not make a triangle; the calculator asks for an angle strictly between them.
Worked examples
Legs 6 and 8
Hypotenuse 10
Hypotenuse c
10
Legs 5 and 5
5√2 ≈ 7.0711
Hypotenuse c
7.0711
Leg 6 opposite a 30° angle
c = 6 / sin 30° = 12
Hypotenuse c
12
Leg 6 next to a 60° angle
c = 6 / cos 60° = 12
Hypotenuse c
12
Decimal legs 1.5 and 2
Hypotenuse 2.5
Hypotenuse c
2.5
Zero leg
Hypotenuse c
—
Angle of 90°
Hypotenuse c
—
Frequently asked questions
What is the formula for the hypotenuse?+
c = √(a² + b²), where a and b are the legs. Square each leg, add, then take the square root.
How do I find the hypotenuse with one side and an angle?+
If the angle is opposite the known leg, divide the leg by the sine of the angle. If the angle is next to the leg, divide by the cosine.
Is the hypotenuse always the longest side?+
Yes. It is opposite the 90° angle, the largest angle, so it is always the largest side.
Can the hypotenuse be a whole number?+
Only when a² + b² is a perfect square, as in 3-4-5 or 5-12-13. Otherwise it is an irrational square root such as √13.
How do I find a leg instead?+
Use the Pythagorean theorem calculator and choose the missing leg: leg = √(c² − other leg²).
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026