Rectangle diagonal
Diagonal: 10
Right triangle calculator
Choose a solving mode. Then enter positive measurements.
Example data
Choose any row to load a known right triangle.
| Side A | Side B | Hypotenuse | Area | Perimeter | Action |
|---|---|---|---|---|---|
| 3 | 4 | 5 | 6 | 12 | |
| 5 | 12 | 13 | 30 | 30 | |
| 8 | 15 | 17 | 60 | 40 | |
| 7 | 24 | 25 | 84 | 56 | |
| 9 | 40 | 41 | 180 | 90 | |
| 12 | 35 | 37 | 210 | 84 | |
| 20 | 21 | 29 | 210 | 70 | |
| 28 | 45 | 53 | 630 | 126 | |
| 33 | 56 | 65 | 924 | 154 | |
| 48 | 55 | 73 | 1320 | 176 |
Advanced geometry tools
These browser tools handle related diagonal calculations.
Square diagonal
Diagonal: 7.071068
Cuboid space diagonal
Diagonal: 13
Roof rafter length
Rafter: 13
Coordinate distance
Distance: 5
Batch hypotenuse calculations
Use commas between the two legs.Four example rows are ready.
Calculation history
Recent successful results stay inside this browser.
No saved calculations yet.
Formula used
c = √(a² + b²)
The hypotenuse equals the square root of both squared legs.
a = √(c² − b²)
A missing leg uses the squared hypotenuse difference.
Area = (a × b) ÷ 2
The legs are perpendicular base and height measurements.
Perimeter = a + b + c
Add every side after finding missing measurements.
How to use this calculator
- Choose the calculation mode matching your known values.
- Enter each positive length, fraction, or scientific value.
- Select the correct unit beside every supplied measurement.
- Choose an output unit and preferred number format.
- Press the calculate button to view complete results.
- Review the diagram, angles, area, perimeter, and steps.
- Copy, print, share, or download the final calculation.
Measure both legs from the same right-angle vertex. Slanted or curved measurements will produce incorrect results.
Understanding the hypotenuse
A right triangle contains one angle measuring exactly ninety degrees. The two sides meeting there are legs. The opposite side is the hypotenuse. It is always the triangle’s longest side.
Why the theorem works
The Pythagorean theorem links all three side lengths. Squaring each leg creates two square areas. Their total equals the square built on the hypotenuse. Therefore, the hypotenuse follows from one square root.
Using different measurement units
Both legs must share a common unit before squaring. This calculator converts each input internally. You may enter feet for one leg and inches for another. The selected output unit controls displayed lengths.
Exact and rounded answers
Some integer inputs create perfect squares. The classic 3-4-5 triangle returns exactly five. Other inputs create irrational roots. The calculator can show a simplified radical and a decimal approximation.
Finding a missing leg
A known hypotenuse changes the operation. Square the hypotenuse and known leg. Subtract the smaller square. Then take the positive square root. The hypotenuse must exceed every leg.
Angles and trigonometry
Right triangles also support sine, cosine, and tangent. These ratios connect an acute angle with side positions. One side and one acute angle can determine the entire triangle.
Practical applications
Builders estimate rafters and diagonal bracing. Designers check rectangular layouts. Surveyors calculate direct distances. Students verify homework. Technicians assess clearances. The same theorem supports each task.
Common mistakes
Do not add unsquared legs. Do not treat the hypotenuse as a leg. Keep measurements positive. Confirm the right angle first. Use enough precision for safety-critical work.
Reliable measurement practices
Measure from consistent endpoints. Avoid rounded source values when possible. Keep unit labels beside every number. Review the diagram before using exported results. Careful inputs always produce more dependable right triangle calculations.
Frequently asked questions
What is a hypotenuse?
The hypotenuse is the side opposite a right angle. It is the longest side in every right triangle.
How do I calculate the hypotenuse?
Square both legs, add those squares, then take the positive square root.
Can both legs use different units?
Yes. The calculator converts each supplied length into a common internal unit before calculating.
Why is the hypotenuse always longest?
Its square equals two positive squared legs combined. Therefore, its length exceeds either individual leg.
How can I find a missing leg?
Subtract the known leg’s square from the hypotenuse square. Then take the positive square root.
What is a Pythagorean triple?
It is three positive integers satisfying a² + b² = c². Examples include 3-4-5 and 5-12-13.
Can side lengths contain fractions?
Yes. Enter ordinary fractions like 3/4 or mixed numbers like 2 1/2.
How accurate is the result?
Internal calculations use floating-point arithmetic. Choose up to fifteen displayed digits for greater precision.