Last updated: July 31, 2026
Missing Side of a Right Triangle Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
c² = a² + b² (Pythagorean theorem)
Where:
- a=Leg a
- b=Leg b
- c=Hypotenuse c
Worked Examples
Find the hypotenuse of a 3-4-5 triangle
Enter the two legs and let the calculator solve for the hypotenuse.
- 1Identify the two known legs: a = 3 and b = 4.
- 2Square each leg: 3² = 9 and 4² = 16.
- 3Add the squares: 9 + 16 = 25.
- 4Take the square root: c = √25 = 5.
Find leg a from leg b and the hypotenuse
Use the leg formula when one leg and the hypotenuse are known.
- 1Treat knownValue1 as the other leg: b = 4.
- 2Treat knownValue2 as the hypotenuse: c = 5.
- 3Compute a² = c² - b² = 25 - 16 = 9.
- 4Take the square root: a = √9 = 3.
Find leg b from leg a and the hypotenuse
The same theorem works symmetrically for the other leg.
- 1Set a = 3 and c = 5 from the known inputs.
- 2Compute b² = c² - a² = 25 - 9 = 16.
- 3Take the square root to isolate the leg.
- 4b = √16 = 4.
Spot an invalid leg problem
The hypotenuse must always be longer than a leg.
- 1Compare the known leg and the supposed hypotenuse.
- 2A valid right triangle needs hypotenuse > leg.
- 3Here 5 is not greater than 5.
- 4The calculator returns an error instead of a non-real answer.
Introduction
This calculator applies the Pythagorean theorem to solve for a missing side in a right triangle. It is ideal when you know two side lengths and want a fast, reliable answer for the third side with consistent 6-decimal precision.
How the Pythagorean Theorem Works
Every right triangle obeys a fixed relationship between its two legs and its hypotenuse.
The theorem states that c² = a² + b².
The hypotenuse c is always the longest side.
The legs a and b meet at the 90° angle.
If both legs are known, add their squares to find the hypotenuse squared.
If one leg and the hypotenuse are known, subtract the leg square from the hypotenuse square.
The final step is always taking a square root to return to a side length.
How to Use This Calculator
The form is intentionally simple so you can solve any of the three sides without extra setup.
Choose which side is missing from the dropdown list.
When solving for the hypotenuse, enter leg a as knownValue1 and leg b as knownValue2.
When solving for leg a, enter leg b as knownValue1 and the hypotenuse as knownValue2.
When solving for leg b, enter leg a as knownValue1 and the hypotenuse as knownValue2.
Review sideA, sideB, and sideC outputs to see the complete triangle.
Use the rounded missingSideValue output for quick copying into homework or engineering notes.
Input Rules and Validation
Right-triangle calculations only make sense when the side data is physically possible.
Both known values must be positive finite numbers.
The missingSide selector must be one of legA, legB, or hypotenuse.
For leg calculations, the second known value must be the hypotenuse.
The hypotenuse must be strictly larger than the known leg.
If c² - leg² is zero or negative, the triangle is invalid.
Invalid input returns a friendly error message instead of an imaginary number.
Worked Right-Triangle Examples
Classic triples show why the theorem is so dependable for manual checking.
3-4-5 gives 5 because 9 + 16 = 25.
5-12-13 gives 13 because 25 + 144 = 169.
8-15-17 gives 17 because 64 + 225 = 289.
Finding a missing leg from 4 and 5 gives 3 because 25 - 16 = 9.
Finding a missing leg from 12 and 13 gives 5 because 169 - 144 = 25.
These triples are useful benchmarks for checking calculator inputs.
Where This Calculation Is Useful
Missing-side calculations appear in school math, trades, engineering, and navigation.
Construction workers use it to verify square corners and bracing lengths.
Homeowners use it when measuring ramps, roofs, and diagonal clearances.
Students use it in geometry, algebra, and trigonometry assignments.
Surveyors use right triangles to infer inaccessible distances.
Fabricators use it for layout, cutting, and frame alignment.
Programmers and designers use the same idea in coordinate geometry and graphics.
Common Mistakes to Avoid
A few simple mix-ups cause most incorrect answers.
Do not place the hypotenuse in knownValue1 when solving for the hypotenuse.
Do not use a shorter value as the hypotenuse when solving for a leg.
Do not forget that the theorem only applies to right triangles.
Do not skip the square root after adding or subtracting the squares.
Do not round too early if you are also checking the work manually.
Do not interpret a validation error as a calculator bug; it usually means the side roles were reversed.
FAQs
Can this calculator find the hypotenuse?
Yes. Choose hypotenuse, then enter the two legs as the known values.
Can it find either leg?
Yes. Choose legA or legB, then enter the other leg first and the hypotenuse second.
Why must the hypotenuse be larger than the other leg?
In a right triangle the hypotenuse is always the longest side, so leg calculations require knownValue2 > knownValue1.
Does the calculator support decimals?
Yes. You can enter decimal side lengths and the outputs are rounded to 6 decimals.
What happens if my inputs do not form a valid right triangle?
The calculator returns an error instead of producing a non-real square root.
Do I need angles for this tool?
No. This calculator only needs the appropriate two side lengths for a right triangle.
Is this the same as a Pythagorean theorem calculator?
Yes. It is a focused Pythagorean theorem calculator designed specifically for solving one missing side.