Recover the unknown leg
Missing Side Calculator
Know the hypotenuse and one leg? Find the missing side of any right triangle instantly, with the formula, the full working, and a live diagram.
- Step-by-step working
- All units supported
- Works offline
- 100% free
Core calculator
Find the Missing Side of a Right Triangle
Result
Enter values to calculate the missing side or verify a triangle.
Show calculation steps
Recent calculations
Looking for the hypotenuse instead? Use the Hypotenuse Calculator.
Formula
The Missing Side Formula
a = √(c² - b²)
To find a missing leg, rearrange the Pythagorean theorem. Start with
a² + b² = c², subtract the known leg squared from both sides, and take
the square root. The result is the length of the unknown leg. This works whether you are solving
for leg a or leg b. The formula is symmetrical.
To find the hypotenuse from two legs, visit the Hypotenuse Calculator.
How it works
How to Find the Missing Side of a Right Triangle
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Enter the hypotenuse
Type the length of the hypotenuse, the longest side opposite the right angle, into the field labeled c.
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Enter the known leg
Type the length of the leg you already know into field a or field b. It does not matter which label you use. The formula is the same either way.
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Choose a unit and precision
Select meters, centimeters, feet, or inches. Adjust decimal places to match the precision your problem requires.
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Read the missing side
The unknown leg appears instantly. Click "Show calculation steps" to see the subtraction and square root written out in full, useful for copying into homework or checking your manual working.
The calculator checks that c is greater than the known leg before computing. If the
hypotenuse value you entered is smaller than the leg, it will flag an error. A valid right triangle
requires the hypotenuse to be the longest side.
Examples
Missing Side Examples with Full Working
Click any example to load it into the calculator above.
5-12-13 triangle
Known hypotenuse 13 and leg 12. Recover the missing leg 5 with a clean integer result.
Basic
8-15-17 triangle
A second integer triple that works well for more advanced practice and verification.
Intermediate
Ladder against a wall
Known ladder length and wall height. Solve for the distance from the wall to the ladder base.
Basic
FAQ
Frequently Asked Questions
Identify whether the missing side is a leg or the hypotenuse. If the hypotenuse is missing,
use c = √(a² + b²). If a leg is missing and you know the hypotenuse
and the other leg, use a = √(c² - b²). Enter the values you know
into the calculator above and it will apply the correct formula and show every step.
For a right triangle, you need at least two side lengths. To find a missing leg, you need the hypotenuse and the other leg. To find the hypotenuse, you need both legs. If you only have one side and one angle, use the Triangle Solver on the Right Triangle Calculator page, which applies trigonometry instead.
Yes, but that is a different calculation. This page focuses on finding a missing leg when the hypotenuse is already known. If you need to find the hypotenuse from two legs, use the Hypotenuse Calculator. Both tools use the same underlying formula, just rearranged differently.
The most common cause is entering a leg value that is larger than or equal to the hypotenuse.
In a valid right triangle, the hypotenuse must always be the longest side. If
c ≤ a or c ≤ b, no real solution exists. Check that the value you
entered as the hypotenuse is actually the longest side of the triangle.
No. The Pythagorean theorem, and this calculator, only applies to right triangles, triangles with exactly one 90-degree angle. For other triangle types, you would need the Law of Cosines or the Law of Sines. The Triangle Solver on the Right Triangle Calculator page handles those cases.
Once you have the missing side, plug all three values back into a² + b² = c².
If the equation holds, the triangle is valid. You can also use the Verify Triangle mode on the
main Right Triangle Calculator. Enter all three sides and
it will confirm whether they form a right triangle.