Introduction
The Triangle Area Calculator helps you find the area of any triangle quickly and easily. The area of a triangle tells you how much space is inside its three sides. The most common formula to calculate it is Area = ½ × base × height. The base is any side of the triangle, and the height is the straight-up distance from that base to the opposite point. This tool does the math for you — just enter your values and get your answer in seconds. Whether you're working on homework, solving geometry problems, or measuring a real-world triangular shape, this calculator saves you time and helps you avoid mistakes.
How to Use Our Triangle Area Calculator
Enter the base and height of your triangle, and this calculator will find the area for you.
Base: Type in the length of the base of your triangle. The base is any one side of the triangle that you want to measure from. You can use any unit, like inches, feet, or centimeters.
Height: Type in the height of your triangle. The height is the straight-up distance from the base to the top point of the triangle. Make sure the height is measured at a right angle (90 degrees) to the base, not along a slanted side.
Result: The calculator will multiply the base by the height and divide by 2 to give you the area of your triangle. The formula used is Area = ½ × base × height. Your answer will be in square units based on the units you entered.
What Is the Area of a Triangle?
The area of a triangle is the amount of space inside its three sides. Think of it as how much flat surface the triangle covers. Area is always measured in square units, like square centimeters (cm²) or square feet (ft²). If you need to calculate area for a four-sided space instead, our Square Footage Calculator can help with that.
Common Formulas for Triangle Area
There are several ways to find the area of a triangle, depending on what information you already know. Here are the most common methods:
Base and Height
The simplest formula is A = ½ × base × height. The base is any one side of the triangle, and the height is the straight-up distance from that base to the opposite corner. The height always meets the base at a right angle (90°). This is the formula most people learn first.
Heron's Formula (Three Sides)
When you know all three side lengths but not the height, you can use Heron's formula. First, find the semi-perimeter: s = (a + b + c) / 2. Then the area is A = √[s(s − a)(s − b)(s − c)]. This method works for any triangle as long as the three sides can actually form a triangle. For that to be true, the sum of any two sides must be greater than the third side. This rule is called the triangle inequality.
Two Sides and an Included Angle (SAS)
If you know two sides and the angle between them, use A = ½ × a × b × sin(γ), where γ is the angle between sides a and b. This formula uses trigonometry — specifically the sine function — to find the area without needing the height directly.
Two Sides and a Non-Included Angle (SSA)
When you know two sides and an angle that is not between them, the calculator uses the Law of Sines to find the missing angles first, then calculates the area. Be aware that this setup sometimes has no solution or two possible solutions, which is known as the ambiguous case.
Two Angles and a Side (ASA and AAS)
If you know two angles, you can always find the third angle because all three angles in a triangle add up to exactly 180°. Once all angles are known, the Law of Sines finds the missing sides, and the area follows. ASA means the known side is between the two known angles. AAS means the known side is not between them. Both methods give one unique answer.
Three Coordinate Points (Shoelace Formula)
When a triangle is drawn on a coordinate grid and you know the (x, y) positions of all three corners, you can use the Shoelace formula: A = ½|x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|. If the result is zero, the three points all lie on the same straight line and do not form a triangle. You can find the length between any two of those points using our Distance Calculator, or locate the center point between two vertices with the Midpoint Calculator.
Special Types of Triangles
Some triangles have shortcuts. An equilateral triangle has three equal sides, and its area is A = (√3 / 4) × a², where a is the side length. A right triangle has one 90° angle, so its two shorter sides (legs) act as the base and height, making the formula simply A = ½ × leg₁ × leg₂. For more detailed calculations involving right triangles — including finding missing sides and angles using the Pythagorean theorem — try our Right Triangle Calculator.
Tips to Remember
- The height must be perpendicular (at a 90° angle) to the base. It is not the same as a slanted side unless the triangle is a right triangle.
- Area is always in square units. If your sides are in centimeters, your area will be in square centimeters.
- When using angles, make sure you know whether they are in degrees or radians. Most everyday problems use degrees.
- The perimeter of a triangle is simply the sum of all three sides: P = a + b + c.
- If you need to find the slope of one of the triangle's sides on a coordinate plane, use our Slope Calculator.
- For help with the square root calculations in Heron's formula or verifying your results, tools like our Percentage Calculator and Sig Fig Calculator can assist with rounding and precision.