How to calculate a triangle's area
Choose the method that matches the values you have: Base & height, Three sides, or Coordinates. The calculation runs in the browser. Select one Unit for all entered lengths or coordinates; the result uses the squared version of that unit.
Choose a calculation method
- Base & height: enter a positive base and its perpendicular height. The calculator uses
A = (1/2) × base × height. - Three sides: enter positive values for Side a, Side b, and Side c. The calculator uses Heron's formula:
s = (a + b + c) / 2, thenA = sqrt(s(s-a)(s-b)(s-c)). - Coordinates: enter the three
(x, y)points. Coordinates may be positive, negative, or zero. The calculator uses the shoelace formula:A = |x1(y2-y3) + x2(y3-y1) + x3(y1-y2)| / 2.
The available units are millimeters, centimeters, meters, kilometers, inches, feet, yards, and miles. Changing the selected mode clears the displayed result.
Calculate and review the result
- Choose Base & height, Three sides, or Coordinates.
- Enter the required values and select a Unit.
- Select Calculate.
- Read the area and the Formula & steps section. A three-side calculation also shows Perimeter and Semi-perimeter.
- Select Copy result or Download result (.txt) to save the displayed result and steps. Select Reset to clear the inputs and result.
Validation and input limits
Enter valid numeric values. Base, height, and side lengths must be positive. Three side lengths must satisfy the triangle inequality: each side must be shorter than the sum of the other two. Coordinate points must not be collinear.
The implementation rejects any absolute input value greater than 1e12. This calculator covers two-dimensional triangle geometry only; it does not calculate angles, classify triangles, or handle 3D shapes.
Privacy and calculation behavior
The triangle arithmetic runs locally in your browser from the values you enter. The calculator implementation does not establish the complete handling of page analytics, tool-view tracking, or subscription-form data, so this page does not make a broader claim about all data requests.
Frequently Asked Questions
What is the formula for the area of a triangle?
The most common formula is A = (1/2) × base × height, where the height is measured perpendicular to the chosen base. If you only know the three side lengths, use Heron's formula instead.
How do I find the area from three side lengths?
Use Heron's formula: compute the semi-perimeter s = (a + b + c) / 2, then A = sqrt(s(s-a)(s-b)(s-c)). The calculator does this automatically and checks that the three lengths can actually form a triangle.
How do I find the area from three coordinate points?
Use the shoelace formula: A = |x1(y2-y3) + x2(y3-y1) + x3(y1-y2)| / 2. This works for any three non-collinear points in a 2D plane, regardless of the triangle's orientation.
Why does the calculator reject some side lengths?
Three lengths only form a valid triangle if each one is shorter than the sum of the other two (the triangle inequality). If that check fails, no real triangle exists and the calculator shows an error instead of a result.
What units does this calculator support?
Millimeters, centimeters, meters, kilometers, inches, feet, yards, and miles. Area is shown in the squared version of the unit you choose, e.g. square meters or square feet.