Side Calculations
Missing Leg From c and a Calculator
This calculator finds the missing leg b of a right triangle when you already know the hypotenuse c and one leg a. Just enter your two known values and get leg b instantly.
Missing Leg From c and a Calculator
This calculator finds Missing leg b using b = √(c² - a²).
Enter inputs to calculate Missing leg b.
Missing leg b
Result-
Solution Steps
Formula: b = √(c² - a²)
What This Tool Solves
Use this page when the hypotenuse and leg a are known, but the other leg is missing. The calculator rearranges the Pythagorean theorem to subtract the known leg from the hypotenuse before taking the square root.
Known values
Hypotenuse c and leg a
Finds
Missing leg b
Main formula
b = √c² - a²
Required check
c must be greater than a
Right Triangle Diagram: Finding Leg b
The diagram marks c and a as the values you already know. The vertical leg b is highlighted as the missing side that this calculator solves.
Diagram Key
Leg a is the known leg along the base of the right triangle.
Leg b is the unknown leg solved by subtracting a^2 from c^2.
Hypotenuse c is the known longest side opposite the right angle.
- c must be the hypotenuse, not one of the legs.
- If c is less than or equal to a, the inputs do not form a valid right triangle.
- The result b uses the same unit as c and a.
Missing Leg b Formula
The formula to find leg b is derived from the Pythagorean theorem (a² + b² = c²). Rearranging for b gives the formula below.
Where c is the hypotenuse (longest side of the right triangle), a is the known leg, and b is the missing leg you’re solving for. Notice the subtraction: you subtract the square of the known leg from the square of the hypotenuse, then take the square root.
How to Find Leg b From c and a
- Confirm that c is the hypotenuse and a is a leg. The hypotenuse is always the longest side.
- Enter the hypotenuse c into the first input field.
- Enter the known leg a into the second input field.
- Click Calculate to find the missing leg.
- Read the result for b, along with the full step-by-step solution.
Example: Find Leg b
Given: c = 13, a = 5. The missing leg of a right triangle with hypotenuse 13 and leg 5 is 12.
Important Check Before Calculating
Before you use this formula, make sure c is greater than a. The hypotenuse is always the longest side of a right triangle. If c equals a, you would get b = 0, which means no triangle exists.
If c is less than a, the expression under the square root becomes negative. That means the two input values cannot describe a real right triangle with c as the hypotenuse.
Use these checks first:
- c is opposite the 90° angle.
- c is greater than a.
- Both values are positive.
- c and a use the same unit.
Where This Calculator Is Useful
This calculator is useful when a diagonal or sloped measurement is known, one perpendicular side is known, and the other perpendicular side is missing. It is the focused tool for the c-and-a case, so every explanation on the page points toward finding b.
It can also help verify measurements. If a measured value for b does not match the calculator result, the triangle may not be right, the hypotenuse may be mislabeled, or one measurement may use a different unit.
Common examples include:
- Finding wall height when ladder length c and ground distance a are known.
- Finding the vertical rise of a slope when the slope length and horizontal run are known.
- Checking a right triangle homework problem that gives c and a.
- Confirming layout measurements for framing, landscaping, ramps, or floor plans.
How to Read the Answer
The output labeled Missing leg b is the length of the other leg that forms the right angle with a. It is not the hypotenuse and should be shorter than c.
If the calculated b is extremely small, your known leg a is very close to the hypotenuse c. That can be valid, but it is worth checking the diagram and the units before using the value.
A valid result should satisfy:
- b is greater than zero.
- b is less than c.
- a² + b² is approximately equal to c².
- The output unit matches the input unit.
Common Mistakes
The most common error is treating c as a leg. In this calculator, c must be the hypotenuse, which is the longest side and the side opposite the right angle.
Another frequent mistake is adding the squares instead of subtracting. Addition finds a hypotenuse; subtraction finds a missing leg from the hypotenuse.
Avoid these mistakes:
- Putting the known leg into the hypotenuse field.
- Using c² + a² instead of c²: a².
- Entering a greater than or equal to c.
- Stopping at b² instead of taking the square root.
- Mixing units such as meters and centimeters.
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 of the right triangle — the longest side, located opposite the 90° angle. It is not a leg. You enter c as one of the two known values in this calculator.
02 What does a mean in this calculator? expand_more
a is one of the two legs of the right triangle. It’s one of the sides that forms the right angle. In this calculator, a is the leg you already know.
03 What does this calculator find? expand_more
This calculator finds the missing leg b. Given hypotenuse c and leg a, it computes b = √c² − a² and shows you the step-by-step solution.
04 Can c be smaller than a? expand_more
No. In a right triangle, the hypotenuse is always the longest side. If c is smaller than a, the values don’t form a valid right triangle. Check which measurement is the hypotenuse before calculating.
05 How do I find b from c and a? expand_more
Square the hypotenuse (c²), square the known leg (a²), subtract a² from c², and take the square root. The formula is b = √c² − a². Or enter your values into this calculator for an instant answer.