Pythagorean Theorem Calculator
Use the Pythagorean theorem to calculate a right triangle hypotenuse from two legs or solve a missing leg from a known hypotenuse and one leg, then check the answer in other length units.
Formula
a^2 + b^2 = c^2
Outputs
c + Missing Leg
Use Cases
Geometry, Trig Prep, Checks
Live calculator
Pythagorean inputs
Calculate hypotenuse from two legs, or calculate a missing leg from one leg and the hypotenuse.
Hypotenuse
5 cm
a squared
9
b squared
16
c squared
25
Missing leg
12
Hypotenuse in other units
| Unit | Converted value | Meaning |
|---|---|---|
| nm | 50,000,000 | Nanometers |
| um | 50,000 | Micrometers |
| mm | 50 | Millimeters |
| cm | 5 | Centimeters |
| dm | 0.5 | Decimeters |
| m | 0.05 | Meters |
| dam | 0.005 | Decameters |
| hm | 0.0005 | Hectometers |
| km | 0.0001 | Kilometers |
| mil | 1,968.5039 | Mils |
| in | 1.9685 | Inches |
| ft | 0.164 | Feet |
| yd | 0.0547 | Yards |
| mi | 0 | Miles |
| nmi | 0 | Nautical miles |
| pt | 141.7323 | Points |
| pc | 11.811 | Picas |
Missing leg in other units
| Unit | Converted value | Meaning |
|---|---|---|
| nm | 120,000,000 | Nanometers |
| um | 120,000 | Micrometers |
| mm | 120 | Millimeters |
| cm | 12 | Centimeters |
| dm | 1.2 | Decimeters |
| m | 0.12 | Meters |
| dam | 0.012 | Decameters |
| hm | 0.0012 | Hectometers |
| km | 0.0001 | Kilometers |
| mil | 4,724.4094 | Mils |
| in | 4.7244 | Inches |
| ft | 0.3937 | Feet |
| yd | 0.1312 | Yards |
| mi | 0.0001 | Miles |
| nmi | 0.0001 | Nautical miles |
| pt | 340.1575 | Points |
| pc | 28.3465 | Picas |
Solve core Pythagorean theorem cases
Find hypotenuse
Use two perpendicular legs to find the longest side of a right triangle.
Find missing leg
Use a known hypotenuse and one leg to calculate the other perpendicular side.
Check squared terms
See a squared, b squared, and c squared so arithmetic mistakes are easier to spot.
Pythagorean theorem formula used on this page
The theorem applies to right triangles where a and b are perpendicular legs and c is the hypotenuse.
Working formulas
Hypotenuse
c = sqrt(a^2 + b^2)
Square both legs, add them, then take the square root.
Missing leg
a = sqrt(c^2 - b^2)
Subtract the known leg squared from the hypotenuse squared.
Symbols
- a, b - legs
- The two sides that meet at the right angle.
- c - hypotenuse
- The longest side, opposite the right angle.
Right-triangle results with squared-term checks
Formula-backed trig basics
- The calculator starts with the values users already know before moving into lesson notes.
- Results keep squared terms, side labels, angles, and trig ratios visible for checking.
- Inputs support decimal measurements for practical right-triangle and layout problems.
- Copy and print controls help students and teachers move results into notes or worksheets.
Right-triangle guardrails
- Missing-leg calculations require the hypotenuse to be longer than the known leg.
- Angle outputs are calculated from the leg ratio and displayed in degrees for classroom readability.
- Related links connect theorem, right-triangle, unit-circle, converter, and guide content.
- FAQ sections explain common mistakes such as mixing legs with hypotenuse or mixing degrees with radians.
Pythagorean support for study and measurement
Students
Check right-triangle homework while seeing the formula path that produced the result.
Teachers
Create examples for theorem lessons, trigonometry introductions, and unit circle prep.
Worksheet builders
Print results and supporting notes for answer keys, examples, and review sheets.
How it works in three quick steps.
Enter both legs
Add leg a and leg b for a right triangle so the calculator can square and add them.
Read the hypotenuse
The hypotenuse is the square root of a squared plus b squared.
Check a missing leg
Enter a known hypotenuse and one known leg to subtract squares and solve the other leg.
Save or print Pythagorean calculations
Copy the result
Copy sides, angles, formulas, and output values into notes or lesson documents.
Print the page
Print calculator inputs, result cards, formulas, FAQs, and related links.
Compare values
Change one side length at a time to see how hypotenuse, area, and angles respond.
About this Pythagorean theorem calculator
Toolarithm's Pythagorean Theorem Calculator is built for the first right-triangle relationship most students learn. It starts with the live side-length inputs, then explains the formula, side labels, and common mistakes below. The result panel shows the hypotenuse calculation and a separate missing-leg workflow so users can check both major theorem cases.
The page treats the theorem as a geometry and trigonometry bridge. It supports distance, diagonals, ladders, ramps, coordinate geometry, and right-triangle prep before sine, cosine, tangent, and unit circle work. Keeping squared terms and unit conversions visible helps users audit each step instead of only copying the final square root result.
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