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Triangle Area Calculator

Calculate a triangle's area from any base and its perpendicular height, with a visible substitution and squared-unit result.

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How to use

  1. 1.Enter the length of any chosen triangle base.
  2. 2.Enter the height measured at 90 degrees to that base and choose the shared length unit.
  3. 3.Select Calculate area, verify the substituted formula, and copy the squared-unit result.

About Triangle Area Calculator

Triangle Area Calculator finds the area enclosed by a triangle when you know one base and the perpendicular height to that base. Enter both positive dimensions, choose millimeters, centimeters, meters, inches, or feet, and select Calculate area. The result shows the squared unit, the exact numbers substituted into one-half base times height, and a copy control. The calculation stays in the browser and does not require an account.

The governing equation is A = bh/2. OpenStax derives it by drawing a diagonal through a rectangle: the diagonal creates two congruent triangles, so each triangle has half the rectangle's area. Wolfram MathWorld independently lists the equivalent base-altitude relationship. The implementation multiplies the entered base by the entered height, divides by two, and rounds only the displayed answer to twelve significant digits. Eight external golden cases cover whole numbers, fractions, decimals, tiny dimensions, and large dimensions.

The height in this equation is not just any second side. It is the shortest perpendicular distance from the line containing the selected base to the opposite vertex. It meets the base line at a 90-degree angle. In an acute triangle that segment falls inside the shape. In an obtuse triangle it can fall outside the visible side, on an extension of the base. The same formula still applies as long as the perpendicular distance is used.

A sloping edge is often mistaken for height. For example, an isosceles or scalene triangle can have two long slanted sides, but neither is automatically perpendicular to the chosen base. If you know only three side lengths, first derive the altitude or use a tool based on Heron's formula. If you know two sides and their included angle, the appropriate relationship is one-half ab sin C. This page intentionally accepts base and perpendicular height so its inputs and assumptions remain unambiguous.

Units must be consistent. A base of 11 centimeters and height of 8 centimeters produces 44 square centimeters. Do not enter one dimension in centimeters and the other in inches while selecting a single unit. Convert one measurement first. Area is written with a squared unit because the multiplication combines two independent lengths. The page labels the answer but does not change the entered magnitudes between measurement systems.

Only finite values greater than zero are accepted. A zero base or height describes a degenerate shape with no enclosed triangular area, so it is rejected rather than presented as an ordinary triangle. The maximum input prevents floating-point overflow. Scientific notation may be accepted by the browser input, and the formatter uses readable ordinary or exponential notation according to the resulting magnitude.

The formula applies to every planar triangle, including right, acute, obtuse, equilateral, isosceles, and scalene triangles, provided the base-altitude pair is valid. For an equilateral triangle where only side length s is known, its height is s√3/2 and substitution gives √3s²/4. This calculator does not infer that special-case height; it asks for the actual perpendicular height so it can also handle non-equilateral shapes.

Use the result for geometry exercises, drawings, landscaping sketches, fabric layouts, rough material estimates, and dimensional checks. Real projects can require allowances for seams, overlap, cutting loss, uneven boundaries, thickness, and measurement uncertainty. Keep enough precision during intermediate work, then round according to the least precise input. For surveying, structural design, or regulated work, rely on verified measurements and the applicable professional method rather than an idealized two-number estimate.

Methodology & sources

Validate finite positive base and perpendicular height values no larger than 1e150, calculate A = base × height ÷ 2 without intermediate rounding, format to twelve significant digits, and attach the square of the selected shared input unit.

Frequently asked questions

What height should I enter?
Use the perpendicular distance from the selected base line to the opposite vertex, not an arbitrary sloping side.
Does the formula work for an obtuse triangle?
Yes. The perpendicular altitude may meet an extension of the base outside the visible triangle, but A = bh/2 still applies.
Why is the result unit squared?
Area multiplies two lengths. Centimeter inputs therefore produce square centimeters, written cm².
Can I calculate an equilateral triangle from one side?
First derive its height as s√3/2, or use the special formula √3s²/4. This page expects base and perpendicular height.

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