Right Triangle Area
Calculate the area of any right triangle from base and height. Get hypotenuse and perimeter with this free online right triangle geometry calculator.
About This Calculator
This free right triangle area calculator computes the area, hypotenuse, and perimeter of a right triangle from its two perpendicular legs (base and height). It is ideal for students learning geometry, carpenters measuring right-angle cuts, DIY enthusiasts planning projects, and professionals in construction, architecture, and engineering who need quick triangle measurements.
The area formula for a right triangle is Area = \u00bd \u00d7 base \u00d7 height, where the base and height are the two legs that form the right angle. Because the legs are naturally perpendicular, no separate height calculation is needed -- simply multiply the two legs and divide by two. The hypotenuse is found using the Pythagorean theorem: c\u00b2 = a\u00b2 + b\u00b2, where c is the longest side. The perimeter is the sum of all three sides: a + b + c. For example, a 3-4-5 right triangle has area = (3 \u00d7 4) / 2 = 6 square units, hypotenuse = 5 units, and perimeter = 12 units.
Regional Notes: This calculator works with any consistent unit system -- metric (cm, m, km) or imperial (inches, feet, yards). In the US, right triangles are commonly used in roofing and carpentry with measurements in feet and inches. In the UK and India, metric units (cm, m) are standard for school geometry and construction projects. The area result displays in square units of whatever unit you enter: cm\u00b2, m\u00b2, in\u00b2, ft\u00b2, and so on.
Frequently Asked Questions
How do you calculate the area of a right triangle?
Area = \u00bd \u00d7 base \u00d7 height. In a right triangle, the two legs are perpendicular so they serve as the base and height directly.
What else does this calculator show?
Besides area, it also computes the hypotenuse using the Pythagorean theorem and the perimeter by summing all three sides.
Can I use this for any triangle?
No, this calculator is specifically for right triangles where one angle is exactly 90\u00b0. For other triangles, use our general triangle area calculator.
What units should I use?
You can use any consistent unit (cm, m, inches, feet). The area will be in square units of whatever unit you enter.
Is this tool free?
Yes, all calculators on Calculy are completely free to use with no registration required.
What is the Pythagorean theorem used for here?
The Pythagorean theorem (a\u00b2 + b\u00b2 = c\u00b2) calculates the hypotenuse from the two legs. It also validates that the entered sides form a valid right triangle.
Can I calculate area if I only know the hypotenuse and one leg?
Yes, use the Pythagorean theorem to find the missing leg: b = \u221a(c\u00b2 \u2212 a\u00b2), then apply Area = \u00bd \u00d7 a \u00d7 b. Our missing side of a right triangle calculator can help with that step.
Why is the area formula different for right triangles?
In a right triangle, the two legs are perpendicular by definition, meaning one leg naturally serves as the base and the other as the height. This simplifies the general A = \u00bd \u00d7 base \u00d7 height formula without needing to identify the perpendicular height separately.