Quick answer
The area of a right triangle is half the product of its legs: A = ½ab. Legs of 3 and 4 give an area of 6.
Enter the two legs. The calculator returns the area.
Related tools: Right Triangle Calculator: Solve a right triangle from its two legs: hypotenuse, angles, area and perimeter. Triangle Area Calculator: Area of a triangle from base and height. Triangle Calculator: Area, perimeter, angles and type of a triangle from its three sides.
How to use the Right Triangle Area Calculator
- Enter leg a (above 0).
- Enter leg b (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Leg a | A number | > 0 |
| Leg b | A number | > 0 |
Formula and method
Formula
A = ½ × a × b
IEEE-754 double precision; shown to at most 6 decimal places.
Half the product of the legs.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Leg a = 3; Leg b = 4.
| Result | Value |
|---|---|
| Area | 6 |
Example 2
Inputs: Leg a = 5.5; Leg b = 2.
| Result | Value |
|---|---|
| Area | 5.5 |
The first line is the headline result (area). IEEE-754 double precision; shown to at most 6 decimal places.
Why half
Two copies of a right triangle form a rectangle of a × b. So the triangle is half of 3 × 4 = 12, which is 6.
Hypotenuse not needed
The area needs only the two legs, which are perpendicular. If you know a leg and the hypotenuse, find the other leg first with the Pythagorean theorem. Legs must be positive.
How the result changes with leg a
Holding every other input at the first worked example, this table changes only leg a. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Leg a | Area |
|---|---|
| 1.5 | 3 |
| 3 | 6 |
| 6 | 12 |
| 12 | 24 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Leg a: entering "0" shows "Leg a must be greater than 0." beside that field and no result.
Choosing between the Right Triangle Area Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Right Triangle Calculator](/math/right-triangle-calculator/) | leg a and leg b | Hypotenuse c |
| [Triangle Area Calculator](/math/triangle-area-calculator/) | base and height | Area |
| [Triangle Calculator](/math/triangle-calculator/) | side a, side b and side c | Area |
| [Right Triangle Side and Angle Calculator](/math/right-triangle-side-angle/) | known sides, leg a and leg b or hypotenuse c | Hypotenuse c |
| [Area Calculator](/math/area-calculator/) | shape and a | Area |
Background: geometry measurements
Geometry results carry units that depend on the quantity: a perimeter or length is in linear units such as cm, an area or surface area is in square units (cm²) and a volume is in cubic units (cm³). Use one length unit for every input, because the calculator multiplies the numbers as given.
Flat (2D) shapes have an area and a perimeter; solids (3D) have a surface area and a volume. Two familiar checks: a circle of radius r has area πr² and circumference 2πr, and a sphere has volume (4/3)πr³ and surface area 4πr².
Assumptions and limitations
- Legs must be positive
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for leg a to confirm this.
Frequently asked questions
What is the area for legs 5 and 12?
Legs of 5 and 12 give an area of ½ × 5 × 12 = 30.
What if I know the hypotenuse?
Find the missing leg first.
Is it the same as a triangle?
A right triangle uses the legs as base and height.
What does the Right Triangle Area Calculator calculate?
Area of a right triangle from its legs. It returns Area.
What formula does the Right Triangle Area Calculator use?
A = ½ × a × b. Half the product of the legs.
What do I need to enter in the right Triangle Area Calculator?
You enter Leg a and Leg b.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Legs must be positive.
What is an example of a right Triangle Area result?
With leg a 3 and leg b 4, the area is 6.
Related calculators
- Right Triangle Calculator — Solve a right triangle from its two legs: hypotenuse, angles, area and perimeter.
- Triangle Area Calculator — Area of a triangle from base and height.
- Triangle Calculator — Area, perimeter, angles and type of a triangle from its three sides.
- Right Triangle Side and Angle Calculator — Complete a right triangle from any two sides.
- Area Calculator — Area of common two-dimensional shapes.
- Area of a Circle Calculator — Area of a circle from its radius, diameter or circumference.
- Triangle Centroid Calculator — Centroid of a triangle from its vertices.
- Parallelogram Area Calculator — Area of a parallelogram.
Sources
- Standard Euclidean geometry formulas (e.g. NIST Digital Library of Mathematical Functions §4, CRC Standard Mathematical Tables)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.