Hypotenuse Calculator
Use this free Hypotenuse Calculator to instantly solve right triangles. Enter two sides, or one side with an angle or area, and get the hypotenuse length immediately. The tool works with local number formats for a smooth experience worldwide.
Number format
Choose how numeric results are displayed. The selected decimal separator (dot or comma) will also be used when parsing input numbers.
Hypotenuse Calculator Guide
This friendly guide helps you get reliable results from the Hypotenuse Calculator. You'll learn what the hypotenuse is, which formulas apply to your inputs, and how to check your work with clear examples. Results appear instantly and the widget accepts your local number format (e.g., commas or dots).
What is the hypotenuse?
In a right triangle (one angle is exactly 90°), the hypotenuse is the longest side, opposite the right angle. The other two sides are commonly labeled a and b, and the hypotenuse is c.
Which formula should I use?
1) Given two sides
If you know both legs a and b:
c = √(a² + b²)
2) Given one angle and one side
Let the known acute angle be θ (in degrees):
- if the known side is adjacent to θ:
c = a / cos(θ) - if the known side is opposite to θ:
c = a / sin(θ)
Tip: angles must be between 0° and 90° for a right triangle's acute angles.
3) Given area and one side
Area of a right triangle is Area = (a × b) / 2. If you know the area A and one leg:
- known leg is a → first find
b = 2A / a, thenc = √(a² + b²) - known leg is b → first find
a = 2A / b, thenc = √(a² + b²)
Step-by-step examples
Example A: two sides
Given: a = 5, b = 12
Compute: c = √(5² + 12²) = √(25 + 144) = √169 = 13
Example B: adjacent side and angle
Given: adjacent a = 7, angle θ = 30°
Compute: c = a / cos(30°) = 7 / (√3/2) ≈ 7 / 0.8660254 ≈ 8.083
Example C: area and one side
Given: area A = 24, leg a = 6
Find b: b = 2A / a = 48 / 6 = 8
Then: c = √(6² + 8²) = √(36 + 64) = √100 = 10
Quick reference (common angles)
| θ (degrees) | sin(θ) | cos(θ) | If opposite known: c = a / sin(θ) | If adjacent known: c = a / cos(θ) |
|---|---|---|---|---|
| 30° | 0.5 | 0.8660254 | c = 2a | c ≈ 1.1547a |
| 45° | 0.7071068 | 0.7071068 | c ≈ 1.4142a | c ≈ 1.4142a |
| 60° | 0.8660254 | 0.5 | c ≈ 1.1547a | c = 2a |
Units, rounding, and input tips
- Units: Use any length unit (cm, m, in, ft). The result will be in the same unit as your inputs as long as you keep them consistent.
- Angles: Enter angles in degrees. If your data is in radians, convert by multiplying by
180/π. - Rounding: For clean reporting, round to a sensible number of decimals (e.g., 2–4). The calculator can display more precision if needed.
- Validation: In a right triangle, each acute angle is between 0° and 90°. If values don't make sense, re-check inputs.
FAQ
Do I need the angle in degrees or radians?
Enter degrees. If you have radians, convert to degrees by degrees = radians × 180/π.
Can I mix units (e.g., one side in cm and the other in inches)?
Avoid mixing units. Convert all lengths to the same unit before calculating to keep the result meaningful.
What if I only know the area and the hypotenuse?
You can solve by expressing one leg in terms of the other using a² + b² = c² and ab = 2A, then solving the resulting quadratic. If available, choose “Area and side” in the widget for a simpler path: provide the area plus either leg.
How accurate are the results?
The calculator uses standard trigonometric and square-root functions with floating-point precision. For most practical tasks, this is more than sufficient. For formal reports, round to an appropriate number of decimals and include your input precision.
Is this tool free and privacy-friendly?
Yes. It's free to use and provides instant results. Inputs are processed client-side by the widget; no sign-up is required.