Pythagorean Theorem Calculator
Calculate the length of the hypotenuse or either leg of a right-angled triangle.
Calculation Type
Triangle Dimensions
Calculator guide
Pythagorean Theorem Calculator
The Pythagorean theorem relates the side lengths of a right triangle. This calculator finds a missing side when the other two sides are known, using a² + b² = c² where c is the hypotenuse opposite the right angle.
How to use the calculator
- 1Identify the right angle and label the side across from it as the hypotenuse. The other two sides are the legs.
- 2Enter the two known side lengths in the correct fields. Use the same unit for both measurements and enter positive values.
- 3Read the missing side and check that the inputs describe a possible right triangle. Round only after keeping enough precision for your use.
Important details to understand
1.Start with the right inputs
Check every number, date, unit, and selected mode before calculating. A correct formula can still give a misleading answer when an input is missing, entered in the wrong unit, or based on a different time period.
2.Know what the calculation includes
The method below describes what this tool uses. Real situations can involve extra rules, costs, calendar conventions, or personal details that are not part of the form, so compare the assumptions with your actual question.
3.Read the unit and rounding
Look at the label as well as the displayed number. Rounding can change the last digits, and results in different units or time periods are not directly comparable until you convert them consistently.
4.Treat the result as a useful check
Use the output to understand a calculation, explore a scenario, or make an initial estimate. When a result affects a formal deadline, a health decision, a contract, or a large payment, confirm it with the relevant source or qualified professional.
How the calculation works
When both legs are known, the hypotenuse is √(a²+b²). When the hypotenuse and one leg are known, the missing leg is √(c²−a²). The hypotenuse must be longer than either leg, or the square-root calculation is not physically valid.
A worked example
For legs of 3 and 4 units, c = √(3²+4²) = √25 = 5 units. This familiar 3-4-5 triangle is a useful check of the formula.
When this calculator is useful
Find diagonal lengths, check right-angle measurements, or solve geometry and construction problems. For physical work, account for measurement tolerances and confirm that the triangle is actually right angled.
Planning ahead
Try a few realistic input values to see how a change in an amount, measurement, date, or rate affects the answer.
Learning the method
Follow the explanation and example to understand which inputs matter and how they are combined.
Checking your own work
Compare the result with a hand calculation, a worksheet, or a trusted source when you need an independent sense check.
Explaining a result
Keep the original inputs and units with the output so another person can understand what was calculated.
Tips for a more reliable answer
- Enter the values from the same source and keep units consistent throughout the calculation.
- Check that you selected the mode or option that matches the question you are trying to answer.
- Use the worked example to confirm you understand the inputs and the kind of result the tool returns.
- Save the inputs with the result so you can review or repeat the calculation later.
Limitations and assumptions
The theorem applies only to right triangles. It does not calculate angles, detect inaccurate measurements, or account for units. Entering values in mixed units or assigning the hypotenuse as a leg gives an incorrect result.
Every result depends on the information entered and the method described above. The calculator cannot confirm that the inputs are complete or that its assumptions match a particular provider, policy, location, body, or real-world situation.
Frequently asked questions
Which side is the hypotenuse?
It is the longest side, directly opposite the right angle.
Can I use inches and feet together?
Convert them to one shared unit first, then enter the lengths.
Why is there no real answer?
The entered hypotenuse may be shorter than a leg, which cannot form a right triangle.
Why might my result differ from another calculator?
Tools can use different assumptions, units, date conventions, included costs, or rounding rules. Compare the inputs and method descriptions before deciding that one result is wrong.
What should I check if the answer looks wrong?
Review the selected mode, each entered value, the units, and any optional fields. Then compare a simple example with the method described in this guide.
Can I rely on the result for an official or high-impact decision?
Use the result as an estimate or explanation and check the limitations listed for this tool. Confirm important decisions with the relevant official source or a qualified professional.