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Rectangle Diagonal Calculator

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How this rectangle diagonal calculator works

Enter the length and width of a rectangle. The calculator finds the diagonal with Diagonal = √(length² + width²). Length 3 and width 4 give √(9 + 16) = 5.0000. The result is shown to four decimal places.

The formula is the Pythagorean theorem. The diagonal is the hypotenuse of a right triangle whose legs are the two sides. Length 5 and width 12 give 13.0000. Length 6 and width 8 give 10.0000. Length 8 and width 15 give 17.0000. Swapping length and width does not change the answer.

Both sides must be finite and at least 0. An empty field or a negative value leaves the result as “--.” Decimals are allowed: 2.5 and 6 give 6.5000. A square with sides 1 and 1 gives √2 ≈ 1.4142. Keep both inputs in the same unit so the diagonal matches that unit.

Check by hand: square each side, add, then take the square root. For 10 and 24: 100 + 576 = 676, and √676 = 26.0000.

Rectangle diagonal examples

Each row is √(length² + width²), rounded to four decimals as on the calculator.

LengthWidthDiagonalWhat it marks
345.00003–4–5 triple
51213.00005–12–13 triple
6810.0000Scaled 3–4–5
81517.00008–15–17 triple
91215.0000Scaled 3–4–5
111.4142Square side 1
2.566.5000Decimal sides
102426.0000Scaled 5–12–13

How to read the result

  • √(L² + W²)

    3 and 4 → diagonal 5.0000.

  • Same units

    Both sides must use one unit; the diagonal matches it.

  • Order does not matter

    Swapping length and width keeps the same diagonal.

  • Four decimals

    A 1×1 square shows 1.4142.

Frequently asked questions

  • How do you find a rectangle’s diagonal?

    Use the Pythagorean theorem. Diagonal = √(length² + width²). Length 3 and width 4 give √(9 + 16) = √25 = 5.0000. The page shows the result to four decimal places.

  • Why does that formula work?

    The diagonal splits the rectangle into two right triangles. The legs are the length and width, and the hypotenuse is the diagonal. Squaring both legs, adding, and taking the square root recovers that hypotenuse.

  • What is a 5–12–13 rectangle diagonal?

    Length 5 and width 12 give √(25 + 144) = √169 = 13.0000. Length 6 and width 8 give 10.0000. Length 8 and width 15 give 17.0000. Those are common Pythagorean triples.

  • Do length and width need the same unit?

    Yes. Enter both in the same unit—metres, centimetres, inches, or feet. The diagonal comes back in that same unit. Mixing units will not give a meaningful length.

  • Can the sides be zero?

    Yes. Values must be finite and at least 0. If one side is 0, the diagonal equals the other side. If both are 0, the diagonal is 0.0000. An empty field leaves the result as “--.”

  • What about a square?

    A square is a rectangle with equal sides. Side 1 and side 1 give √2 ≈ 1.4142. Side 9 and side 12 still use the same formula and give 15.0000.

  • Can I enter decimals?

    Yes. Length 2.5 and width 6 give √(6.25 + 36) = √42.25 = 6.5000. Any non-negative finite numbers are accepted.

  • Does the calculator care which side is length or width?

    No. Swapping the two boxes does not change the diagonal, because length² + width² is the same either way. 3 and 4 give 5.0000 whether 3 is length or width.

  • How precise is the answer?

    The diagonal is fixed at four decimal places. Exact triples such as 3–4–5 show 5.0000. √2 for a 1×1 square shows 1.4142.

  • How do I check the answer by hand?

    Square each side, add the squares, then take the square root. For 10 and 24: 100 + 576 = 676, and √676 = 26.0000.