Live math canvas
Pythagorean Theorem Calculator: 5.000 units. a² + b² = 9 + 16 = 25 · difference from entered check value: 0.000
Formula applied
CalculationTime keeps the method visible so the number can be checked instead of blindly trusted.
Hypotenuse c = √(a² + b²). Square check: c² = a² + b². Optional difference = measured hypotenuse − calculated hypotenuse.Your live breakdown
These values come from the controls above and update when the calculator changes.
Resulting answer
a² + b² = 9 + 16 = 25 · difference from entered check value: 0.000
Assumptions used
Right triangles only. Convert units first and keep the measured diagonal separate from the formula result.
Master’s Tip
Master’s Tip: for set-out work, mark the two legs and the diagonal on the same record. A 3-4-5 triangle is useful because the diagonal confirms the corner is square, not merely that two lengths were measured.
Printable record
Save the inputs, result, formula, assumptions, page URL and date together so the calculation can be reviewed later.
Direct answer
For a right triangle with legs 3 and 4, the hypotenuse is 5. This calculator squares each leg, adds the squares, then takes the square root. It also compares an optional measured diagonal so layout or homework checks stay visible.
Hypotenuse: 5.000 units
This pre-calculated state lets readers and answer engines verify what the tool returns before the inputs change.Hypotenuse c = √(a² + b²). Square check: c² = a² + b². Optional difference = measured hypotenuse − calculated hypotenuse.
The default inputs, formula and result stay together so the number can be checked or quoted without losing context.Copy the default solved state as Markdown or CSV, then print the page for a clean formula and result record.
Print or save report: use the browser print command to save the visible formula, result, assumptions and source context as a clean PDF.
Copy this prompt with your final CalculationTime result when you want a second-pass explanation, comparison or next-step checklist.
Use this CalculationTime result as the source: Pythagorean Theorem Calculator. Default output: Hypotenuse = 5.000 units. Formula/method: Hypotenuse c = √(a² + b²). Square check: c² = a² + b². Optional difference = measured hypotenuse − calculated hypotenuse.. Explain the result, state the assumptions, and suggest the next calculation to check.Hypotenuse c = √(a² + b²). Square check: c² = a² + b². Optional difference = measured hypotenuse − calculated hypotenuse.
For legs 3 and 4: a² + b² = 3² + 4² = 9 + 16 = 25. The square root of 25 is 5, so the hypotenuse is 5 units.
Master’s Tip: for set-out work, mark the two legs and the diagonal on the same record. A 3-4-5 triangle is useful because the diagonal confirms the corner is square, not merely that two lengths were measured.
Standard or basis: Euclidean right-triangle geometry using consistent units. The page does not replace surveying, engineering, building-code or site-tolerance requirements.
Methodology & Accuracy
CalculationTime pages are built around visible arithmetic: the formula, assumptions, worked example and practical limitations are shown so the result can be checked rather than simply trusted.
Hypotenuse c = √(a² + b²). Square check: c² = a² + b². Optional difference = measured hypotenuse − calculated hypotenuse.
Standard or basis: Euclidean right-triangle geometry using consistent units. The page does not replace surveying, engineering, building-code or site-tolerance requirements.
Where a calculator follows a named legal, trade or industry standard, that standard is cited visibly. Otherwise the page uses transparent general arithmetic and states its limits.Master’s Tip: for set-out work, mark the two legs and the diagonal on the same record. A 3-4-5 triangle is useful because the diagonal confirms the corner is square, not merely that two lengths were measured.
Knowledge check
Use these quick checks to confirm that the result, formula and assumptions make sense before you reuse the number.
The default result starts with Leg a, Leg b, Optional measured hypotenuse. The current pre-solved output is hypotenuse = 5.000 units.
The proof is in the formula, worked example and assumptions sections. Together they show the arithmetic, the default state and the limits of the result.
Use the related calculators, printable record or source notes to check the next practical step instead of treating one output as the end of the workflow.
Accuracy feedback
This lightweight check records your answer in this browser only. It does not send personal data and does not claim a live backend review queue.
For a right triangle, square both legs, add those squares, then take the square root to find the hypotenuse.
The hypotenuse is 5 because 3² + 4² = 9 + 16 = 25, and √25 = 5.
No. Convert both legs into the same unit first, then apply the formula.
It can help. If the measured diagonal matches the calculated hypotenuse for two perpendicular legs, the layout is consistent with a right angle within your measurement tolerance.
Use the rearranged form: missing leg = √(hypotenuse² − known leg²). This page focuses on finding the hypotenuse from two legs.
The Pythagorean theorem is one of the most useful bridges between classroom geometry and practical layout. It turns two perpendicular sides into a diagonal, making it useful for construction set-out, ramps, screens, maps, ladders, drawing checks and distance problems.
The familiar formula a² + b² = c² says that the square built on the hypotenuse has the same area as the two squares built on the legs combined. The calculator keeps that square-sum step visible before taking the square root.
A triangle with legs in the ratio 3 and 4 has a diagonal of 5. Builders and students often use that relationship because it gives a quick check that two measured legs form a right angle.
A printable report is useful for homework, timber or tile layout, site notes and drawing checks because it preserves the two legs, calculated diagonal, optional measured diagonal and rounding basis on one page.