CalculationTime

Pythagorean Theorem Calculator

Find the hypotenuse of a right triangle from two legs, with square-sum proof, optional check length and a printable classroom or layout record.

Live math canvas

Your numbers, formula and explanation together

Pythagorean Theorem Calculator: 15 diagonal length. Pythagorean Theorem Calculator uses the declared inputs to produce a transparent default result. Leg a: 3 units; Leg b: 4 units; Optional measured hypotenuse: 5 units; Round display to: 3 decimal places; primary comparison: 3 and 4.

Formula applied

The exact method behind this answer

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.
  1. Apply the formulaHypotenuse c = √(a² + b²). Square check: c² = a² + b². Optional difference = measured hypotenuse − calculated hypotenuse.15 diagonal lengthPythagorean Theorem Calculator uses the declared inputs to produce a transparent default result. Leg a: 3 units; Leg b: 4 units; Optional measured hypotenuse: 5 units; Round display to: 3 decimal places; primary comparison: 3 and 4.

Your live breakdown

Current inputs in the calculation

These values come from the controls above and update when the calculator changes.

Leg a
3 units
One perpendicular side of the right triangle.
Leg b
4 units
The other perpendicular side of the right triangle.
Optional measured hypotenuse
5 units
Enter a measured diagonal to compare against the calculated hypotenuse, or leave 0 for no check.
Round display to
3 decimal places
Controls display rounding only; the formula uses full precision.

Resulting answer

15 diagonal length

Pythagorean Theorem Calculator uses the declared inputs to produce a transparent default result. Leg a: 3 units; Leg b: 4 units; Optional measured hypotenuse: 5 units; Round display to: 3 decimal places; primary comparison: 3 and 4.

Answer
15 diagonal length
Live support
Pythagorean Theorem Calculator uses the declared inputs to produce a transparent default result. Leg a: 3 units; Leg b: 4 units; Optional measured hypotenuse: 5 units; Round display to: 3 decimal places; primary comparison: 3 and 4.

Assumptions used

What this answer assumes

Right triangles only. Convert units first and keep the measured diagonal separate from the formula result.

  • The triangle is a right triangle: leg a and leg b meet at a 90° angle.
  • Both legs use the same unit. Do not mix inches and centimetres without converting first.
  • The optional measured hypotenuse is a comparison line, not an input to the theorem result.
  • Rounding affects the displayed answer only; keep more precision for layout, machining, engineering or assessed work.

Master’s Tip

How to use the result well

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

What belongs in the saved calculation

Save the inputs, result, formula, assumptions, page URL and date together so the calculation can be reviewed later.

Leg a
3 units
One perpendicular side of the right triangle.
Leg b
4 units
The other perpendicular side of the right triangle.
Optional measured hypotenuse
5 units
Enter a measured diagonal to compare against the calculated hypotenuse, or leave 0 for no check.
Round display to
3 decimal places
Controls display rounding only; the formula uses full precision.

Embeddable calculator

Embed this calculator

Copy a clean iframe version with the required CalculationTime attribution link built in.

Formula

Hypotenuse c = √(a² + b²). Square check: c² = a² + b². Optional difference = measured hypotenuse − calculated hypotenuse.

Worked example

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.

Professional note

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.

Regional and unit assumptions

Standard or basis: Euclidean right-triangle geometry using consistent units. The page does not replace surveying, engineering, building-code or site-tolerance requirements.

Assumptions and limitations

Methodology & Accuracy

How this calculator is checked

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.

Formula used

Hypotenuse c = √(a² + b²). Square check: c² = a² + b². Optional difference = measured hypotenuse − calculated hypotenuse.

Standard or basis

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

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.

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Questions

How do you use the Pythagorean theorem?

For a right triangle, square both legs, add those squares, then take the square root to find the hypotenuse.

What is the hypotenuse for 3 and 4?

The hypotenuse is 5 because 3² + 4² = 9 + 16 = 25, and √25 = 5.

Can I use different units for the two legs?

No. Convert both legs into the same unit first, then apply the formula.

Does this prove my corner is square?

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.

What if I know the hypotenuse and one leg?

Use the rearranged form: missing leg = √(hypotenuse² − known leg²). This page focuses on finding the hypotenuse from two legs.

Calculation note

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 theorem is a square-area statement

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.

The 3-4-5 triangle is a practical squaring tool

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.

Print the diagonal with the assumptions

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.

Sources and further readingEncyclopaedia Britannica: Pythagorean theoremKhan Academy: Pythagorean theorem