Area of a Right Angle Triangle Calculator

Enter any two of the three sides — the two legs or one leg and the hypotenuse — to get area, perimeter, and step-by-step working instantly.

Unit:
Leg a (base)
cm
Leg b (height)
cm
Hypotenuse c
cm

Enter any two values — the third updates automatically.

Triangle Diagram

Right Triangle Formulas

Area

A = ½ × a × b

Half of base times height — both perpendicular legs.

Pythagorean Theorem

c = √(a² + b²)

Find the hypotenuse from both legs.

Perimeter

P = a + b + c

Sum of all three sides.

From c & a

b = √(c² − a²)

Find missing leg from hypotenuse and one leg.

Worked Example — 3-4-5 Right Triangle

Right triangle with legs 3 cm and 4 cm (the famous Pythagorean triple):

Given: a = 3 cm, b = 4 cm
Step 1: c = √(3² + 4²) = √(9 + 16) = √25 = 5 cm
Step 2: A = ½ × 3 × 4 = 6 cm²
Step 3: P = 3 + 4 + 5 = 12 cm
Answer: Area = 6 cm², Perimeter = 12 cm

Famous Pythagorean Triples

Leg a Leg b Hypotenuse Area Perimeter
3 cm 4 cm 5 cm 6 cm² 12 cm
5 cm 12 cm 13 cm 30 cm² 30 cm
8 cm 15 cm 17 cm 60 cm² 40 cm
9 m 40 m 41 m 180 m² 90 m
6 m 8 m 10 m 24 m² 24 m

Real-World Applications

🏗️

Construction

Roof pitch calculations, stair stringers, and rafter lengths all rely on right triangle geometry.

📐

Navigation

Distance and direction problems — find the shortest path between two points using right triangle geometry.

⚙️

Engineering

Ramps, inclined planes, and force resolution into components all involve right triangle calculations.

🏔️

Surveying

Height measurement using trigonometry — measure horizontal distance and angle to find vertical height.

🎮

Game Development

Collision detection, movement vectors, and 2D distance calculations use the Pythagorean theorem constantly.

Frequently Asked Questions

What is the area formula for a right triangle?
A = ½ × a × b where a and b are the two perpendicular legs — not the hypotenuse. The right angle itself is formed between these two legs, making them the base and height of the triangle.
What is the Pythagorean theorem?
c² = a² + b², so hypotenuse c = √(a² + b²). This only works for right triangles. It states that the area of the square on the hypotenuse equals the sum of the areas of the squares on the other two sides.
How do you find area if you only know the hypotenuse and one leg?
First find the missing leg: b = √(c² − a²), then apply A = ½ab. For example, hypotenuse = 5 cm and leg a = 3 cm: b = √(25−9) = √16 = 4 cm, so A = ½ × 3 × 4 = 6 cm².
What are Pythagorean triples?
Sets of positive integers (a, b, c) where a² + b² = c². Common ones: (3,4,5), (5,12,13), (8,15,17), (9,40,41). Multiplying any triple by a constant gives another valid triple — e.g., 2×(3,4,5) = (6,8,10).
Why is the area ½ × base × height for a right triangle?
A right triangle is exactly half of a rectangle with sides a and b. Draw the diagonal of any rectangle — it creates two identical right triangles. Rectangle area = a × b, so each triangle = ½ab. The ½ factor applies to all triangles, not just right triangles.

Related Area Calculators

Circle Semicircle Square Rectangle Parallelogram Rhombus Trapezium Scalene Triangle Right Angle Triangle Equilateral Triangle Isosceles Triangle Regular Hexagon Sector & Segment