Pythagoras Theorem Calculator
Solve a² + b² = c² for hypotenuse or either leg; optional 3D space diagonal. Free MyCalcsWorld geometry tool with mode-aware fields.
Results
Hypotenuse c
- Perimeter
- 12
Educational estimates · not financial advice · free, no signup
Formula / how it works
a² + b² = c². For 3D: √(a²+b²+c²) is the space diagonal.
Detailed guide
What it is, how to use it, how to read the numbers, common mistakes, a worked example, formulas, and FAQs.
What this calculator is
Pythagoras’ theorem is the workhorse of right-triangle geometry. MyCalcsWorld’s Pythagoras Calculator lets you pick a mode — find hypotenuse c, find leg a, find leg b, or compute a 3D space diagonal — and only shows the fields that mode needs (unused sides stay hidden). Enter the known sides, read the unknown, and optionally confirm with the classic 3-4-5 check. Built for homework, DIY squaring, and quick engineering sketches under Euclidean assumptions. Educational math — contest proofs may still want exact radicals on paper.
When to use / who it helps
- Homework or exam practice on right triangles.
- DIY squaring a corner (does 3-4-5 hold on your tape measures?).
- Finding a missing leg when hypotenuse and one leg are known.
- Computing a room or box space diagonal in 3D mode.
- Checking calculator work against a hand-derived radical form.
How to use
Steps
- Choose Mode (find hypotenuse, find a leg, or 3D diagonal).
- Enter only the sides shown for that mode — hidden fields are unused on purpose.
- Read the primary unknown (c, a, b, or space diagonal).
- Optional: switch mode and re-enter to solve a different unknown.
- Compare decimals to an exact radical when your course requires it.
- Use Related tools (Heron, distance) if the triangle is not right-angled.
How to interpret results
- In hyp mode, c is always the longest side of a right triangle.
- In leg modes, the tool rejects inputs where hypotenuse ≤ known leg.
- 3D mode returns the space diagonal through a rectangular box.
- Displayed precision is rounded; re-derive exact forms for proofs.
- Educational geometry only — survey work needs real measurement tolerances.
Common mistakes & gotchas
- Using a non-hypotenuse side as c — c must be the longest side in 2D modes.
- Forgetting that leg modes require c > the known leg.
- Mixing units (cm vs m) across a and b.
- Expecting exact √ forms when the UI shows decimals.
- Applying 2D Pythagoras to non-right triangles without more trig.
Worked example
Worked example — 3-4-5 right triangle
- Mode: Find hypotenuse c from legs a & b.
- a = 3; b = 4.
- c = √(3² + 4²) = √(9+16) = √25 = 5.
- Enter 3 and 4 on this page in hyp mode to mirror the live panel.
- Optional: switch to leg-a mode with b=4, c=5 to recover a=3.
Result: Hypotenuse c = 5 for the classic 3-4-5 triple.
Want these demo numbers in the form? Tap Try example above the Calculate button.
How to calculate / formula
a² + b² = c². For 3D: √(a²+b²+c²) is the space diagonal.
Frequently asked questions
What is the Pythagorean theorem?
In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs: a² + b² = c².
Why do some fields disappear?
Mode-aware visibleWhen hides unused sides so you do not type a value that the selected solve path ignores.
Can I solve for a leg?
Yes — choose Find leg a or Find leg b and enter the other leg plus the hypotenuse (which must be longer).
What does 3D mode do?
It computes the space diagonal √(a²+b²+c²) of a rectangular box with edges a, b, c.
Why don’t I see exact radicals?
The numeric engine shows decimals. Exams often still want √ forms — convert on paper when required.
Does this work for non-right triangles?
Not with this identity alone. Use the law of cosines / Heron tools for general triangles.
How precise are results?
Internal math uses floating point; display uses fixed precision. Re-check proofs with exact arithmetic.
Is this the same as Pythagoras 3D demo pages?
Related family — this form focuses on numeric solves with mode-aware inputs; demo pages emphasize visualization.
What does the Pythagoras Theorem Calculator on MyCalcsWorld actually compute?
Find the hypotenuse or either leg of a right triangle; optional 3D space diagonal. You enter Mode, Side a (leg), Side b (leg), Side c (hypotenuse), and the result panel updates in your browser — free, no signup. Below the form you will find when-to-use tips, common mistakes, a worked example, formula notes, and FAQs for this tool.
Questions about this tool? Contact MyCalcsWorld · mycalcsworldcontact