Find a right triangle hypotenuse with squared working, area, perimeter, unit guidance and reasonableness checks.
Choose an example or type the known values, then calculate to see the answer and working.
The two entered sides meet at the marked right angle.
Estimate the sign, scale, range or likely form of the answer before calculating. A prediction makes an input error easier to notice.
Square both perpendicular lengths: 6² = 36 and 8² = 64.
Add the squares: c² = 36 + 64 = 100.
Take the positive square root because length is positive: c = √100 = 10 cm.
Check the bounds: 10 is greater than 8 and less than 6 + 8 = 14.
Pythagoras' theorem links the three side lengths of a right-angled triangle. This calculator accepts the two perpendicular sides and finds the hypotenuse, area and perimeter. The right-angle condition is essential. The longest drawn side is not enough evidence; mark the ninety-degree angle and identify the opposite side as the hypotenuse before entering measurements.
Use it when two known positive lengths meet at a right angle and the missing length is the hypotenuse. This specific mode does not rearrange the formula to find a shorter side. Convert both inputs to the same unit first. If the diagram is not right-angled, another geometric relationship is required even if the numbers produce a plausible square root.
The equation is not a general rule for all triangles. It describes the squared relationship created by perpendicular sides. Without that condition, the calculated length can be geometrically wrong.
It must be longer than either perpendicular side and shorter than their sum. These bounds provide an immediate check before any detailed substitution.
Lengths squared create square units inside the calculation, but the final square root returns a length unit. Area remains in square units because no final root is taken.
| Mistake | Why it fails | Better check |
|---|---|---|
| Adding sides before squaring | The expression (a + b)² contains an extra cross term and is not Pythagoras' theorem. | Square each perpendicular side separately, then add. |
| Using the hypotenuse as an input leg | The calculator then finds a different and oversized diagonal. | Enter only the two sides touching the right angle. |
| Dropping units | A numerical length cannot show whether the result is centimetres or metres. | Convert first and restore the common length unit after the root. |
Yes. A square diagonal divides the square into right triangles, so enter the equal side length for both perpendicular inputs.
An equation for c squared has positive and negative algebraic roots, but a physical side length is positive.
Rearrange to a = √(c² - b²). This page is intentionally fixed to finding the hypotenuse from two perpendicular sides.
The result points to related practice, but the best next step depends on what the learner could explain without help.