Case 1
- Leg a
- 3
- Leg b
- 4
6.0000
Open with these valuesRight Triangle Calculator
6.0000units²
Result: 6.0000 units²The two legs meet at the right angle, so they are base and height at once: the area is ½ × a × b. Legs of 3 and 4 give 6 square units, a hypotenuse of 5, a perimeter of 12 and angles of 36.87° and 53.13°. Every figure follows from those two lengths.
The numbers at a glance
Held fixed: Leg a 3.000.
| Leg b | Result |
|---|---|
| 1.000 | 1.5000 |
| 2.000 | 3.0000 |
| 3.000 | 4.5000 |
| 4.000Your value | 6.0000 |
| 5.000 | 7.5000 |
| 6.000 | 9.0000 |
| 7.000 | 10.5000 |
| 8.000 | 12.0000 |
Worked examples
Case 2
- Leg a
- 7
- Leg b
- 24
84.0000
Open with these valuesCase 3
- Leg a
- 2.5
- Leg b
- 6
7.5000
Open with these valuesHow it's calculated
A = ½ × a × b
- StepMeasure the two legs — the sides that meet at the right angle.
- StepEnter both in the same length unit.
- ResultRead the area; the table adds hypotenuse, perimeter and angles.
Reference table
| Legs a, b | Hypotenuse · perimeter · acute angles | Area |
|---|---|---|
| 1, 1 | 1.4142 · 3.4142 · 45° and 45° | 0.5000 |
| 2.5, 6 | 6.5 · 15 · 22.62° and 67.38° | 7.5000 |
| 3, 4 | 5 · 12 · 36.87° and 53.13° | 6.0000 |
| 5, 12 | 13 · 30 · 22.62° and 67.38° | 30.0000 |
| 7, 24 | 25 · 56 · 16.26° and 73.74° | 84.0000 |
Questions
How do I calculate the area of a right triangle?
Multiply the two legs and halve the result: area = ½ × a × b. The legs are the base and the height, because they meet at a right angle. Legs of 3 and 4 give ½ × 3 × 4 = 6 square units.
How do I find the hypotenuse from the legs?
Square each leg, add the two squares and take the square root: hypotenuse = √(a² + b²). For legs of 3 and 4 that is √25 = 5. The hypotenuse is always the longest side, because it sits opposite the 90° corner.
How do I find the angles from the legs?
Use the inverse tangent: the angle opposite leg a is atan(a ÷ b), the angle opposite leg b is atan(b ÷ a). For legs of 3 and 4 these are 36.87° and 53.13°. The two acute angles always add to 90°, so one gives the other.
Why is the 3-4-5 triangle special?
It is the smallest right triangle with whole-number sides: 3² + 4² = 9 + 16 = 25 = 5². Builders mark 3 units along one side and 4 along the other, and if the diagonal measures exactly 5 the corner is a true right angle.
What units does the right triangle calculator use?
The lengths are unit-agnostic: enter the legs in centimetres, metres or inches and the area comes back in that unit squared. Hypotenuse and perimeter stay in the entered unit, and the two angles are always in degrees.
Sources and last check
Information, not professional advice.