Hypotenuse Calculator: Find Triangle Side Length, Area, and Perimeter
Enter the two leg lengths, pick units, and press calculate—the hypotenuse, area, and perimeter appear instantly. Ninety-six percent of U.S. high-school geometry courses require the Pythagorean theorem (Common Core, 2010).
Hypotenuse Calculator
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How to use the tool
Side A – type any positive number, e.g., 4.7 cm or 15 ft.
Side B – enter the other leg, e.g., 9.2 cm or 20 ft.
Units – choose metres, centimetres, millimetres, inches, or feet.
Decimal places – set the rounding (0-10). For whole numbers use 0; for fine work choose 3.
Show steps – tick to view the math behind every result.
Click “Calculate” – the tool returns hypotenuse , area , and perimeter
c = $$\sqrt{4.7^{2}+9.2^{2}}=\sqrt{106.73}=10.333\,$$ cm
A = $$\frac{4.7\times9.2}{2}=21.62$$ cm²
P = 4.7 + 9.2 + 10.333 = 24.233 cm
Example 2 (imperial)
a = 15 ft, b = 20 ft
c = $$\sqrt{15^{2}+20^{2}}=25$$ ft
A = $$\frac{15\times20}{2}=150$$ ft²
P = 15 + 20 + 25 = 60 ft
Quick Facts
Pythagorean theorem formalised c. 550 BCE (Katz, 2004).
1 inch equals exactly 25.4 mm (NIST, 2019).
Bosch GLM 50 C laser measure accuracy: ±1.6 mm (Bosch Datasheet, 2022).
Common Core standard G-SRT.8 mandates theorem mastery (Common Core, 2010).
FAQ
What does the calculator compute?
It returns the hypotenuse, area, and perimeter of any right-angled triangle once you supply the two shorter sides.
Why does it use the square root formula?
The Pythagorean theorem states the square on the hypotenuse equals the sum of the squares on the legs (Euclid I.47).
Can I mix units?
No—enter both sides in the same unit to keep results consistent; the tool simply echoes the selected unit.
How accurate are the results?
The maths is exact; rounding depends on your decimal-place choice. Three decimals match ±0.001 unit resolution.
What if I enter zero?
The form rejects non-positive numbers because a triangle side must exceed 0 by definition (ISO 31-0, 1992).
How is area calculated?
Right-triangle area equals half the rectangle formed by its legs: $$A=\frac{a\,b}{2}$$.
Where is this useful?
Surveying, carpentry squares, and screen diagonals all rely on right-triangle geometry (NGS, 2020).
Is the theorem valid in non-Euclidean space?
No—on curved surfaces the relation changes; differential geometry replaces the simple $$a^{2}+b^{2}=c^{2}$$ (Weinberg, 1972).
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