Side Calculations
Missing Leg From c and b Calculator
This calculator finds the missing leg a of a right triangle when you know the hypotenuse c and the other leg b. Enter your values above to get the result with a full step-by-step breakdown.
Missing Leg From c and b Calculator
This calculator finds Missing leg a using a = √(c² - b²).
Enter inputs to calculate Missing leg a.
Missing leg a
Result-
Solution Steps
Formula: a = √(c² - b²)
What This Tool Solves
Use this page when you know the hypotenuse and leg b, but need leg a. It keeps the known side b separate from the unknown side a so the formula and result match the labels on your triangle.
Known values
Hypotenuse c and leg b
Finds
Missing leg a
Main formula
a = √c² - b²
Required check
c must be greater than b
Right Triangle Diagram: Finding Leg a
The diagram shows c as the known hypotenuse and b as the known leg. The base leg a is highlighted as the missing value returned by the calculator.
Diagram Key
Leg a is the unknown base leg solved from c and b.
Leg b is the known leg that forms the right angle with a.
Hypotenuse c is the known longest side of the right triangle.
- The hypotenuse c must be the longest side in the input pair.
- If c is less than or equal to b, re-check which value is the hypotenuse.
- The calculated a has the same unit as the values you entered.
Missing Leg a Formula
Starting from the Pythagorean theorem (a² + b² = c²), solve for a to get the formula below.
Where c is the hypotenuse (the longest side, opposite the right angle), b is the known leg, and a is the missing leg you want to find. The key operation is subtraction: square the hypotenuse, subtract the square of the known leg, then take the square root of what’s left.
How to Find Leg a From c and b
- Make sure you’ve correctly identified the hypotenuse (c) and the known leg (b). The hypotenuse is always across from the 90° angle.
- Enter the hypotenuse c into the first input field.
- Enter the known leg b into the second input field.
- Click Calculate to find leg a.
- Review the result for a and the step-by-step work shown below.
Example: Find Leg a
Given: c = 10, b = 6. The missing leg of a right triangle with hypotenuse 10 and leg 6 is 8.
Important Check Before Calculating
The hypotenuse c must be greater than b for the calculation to work. In every right triangle, the hypotenuse is the longest side. If c equals b, the formula gives a = 0, which means no triangle can be formed.
If c is less than b, the expression under the square root becomes negative and there is no real side length for a. In that case, re-check which side is opposite the 90° angle.
Use these checks first:
- c is the side opposite the right angle.
- c is greater than b.
- Both inputs are positive numbers.
- c and b use the same measurement unit.
Where This Calculator Is Useful
This calculator is the right tool when you know the hypotenuse and leg b and need to find leg a. It is especially helpful when your diagram labels the known leg as b and the unknown base or height as a.
The page also works as a measurement check. If the calculated side a is very different from a measured side, the triangle may not include a true 90° angle or one of the known values may have been copied incorrectly.
Common examples include:
- Finding a base distance when the slope length c and height b are known.
- Finding a vertical height when the hypotenuse and horizontal distance are known.
- Solving geometry problems that give c and b and ask for a.
- Checking construction, mapping, or floor-plan measurements that form a right triangle.
How to Read the Answer
The output labeled Missing leg a is the other side that forms the right angle with b. It should be shorter than the hypotenuse c and greater than zero.
If the result is close to c, the known leg b is relatively small. If the result is close to zero, b is almost as long as c. Both can happen, but the input labels should be checked before using the answer.
A valid result should satisfy:
- a is greater than zero.
- a is less than c.
- a² + b² is approximately equal to c².
- The output unit matches the unit used for c and b.
Common Mistakes
The biggest risk is swapping the hypotenuse with a leg. This calculator assumes c is already the longest side, so a mislabeled c value will make the result incorrect.
A second common issue is using the hypotenuse formula by mistake. To find a missing leg, you subtract the known leg square from the hypotenuse square, then take the square root.
Avoid these mistakes:
- Entering leg b as the hypotenuse c.
- Using c² + b² instead of c²: b².
- Entering b greater than or equal to c.
- Forgetting the square root after subtracting.
- Combining measurements that use different units.
Related Calculators
Frequently Asked Questions
Answers to the most common right-triangle solving questions.
01 What does c mean in this calculator? expand_more
c is the hypotenuse — the longest side of the right triangle, opposite the 90° angle. In this calculator, you enter c as one of your two known values.
02 What does b mean in this calculator? expand_more
b is one of the two legs of the right triangle. It’s a side that forms the right angle. Here, b is the leg you already know, and the calculator uses it along with c to find the missing leg a.
03 What does this calculator find? expand_more
It finds the missing leg a. You provide the hypotenuse (c) and one leg (b), and the calculator applies the formula a = √c² − b² to give you the unknown leg with a step-by-step solution.
04 Can c be smaller than b? expand_more
No. The hypotenuse is always the longest side in a right triangle. If your value for c is smaller than b, the inputs don’t represent a valid right triangle. Re-check which measurement corresponds to the hypotenuse.
05 How do I find a from c and b? expand_more
Square the hypotenuse (c²), square the known leg (b²), subtract b² from c², and take the square root of the result. The formula is a = √c² − b². You can also just enter your values into this calculator to get the answer automatically.