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Triangle Area Calculator

Calculate the area of a triangle using base and height. The classic formula A = ½ × base × height.

Reviewed by Chase FloiedUpdated

This free online triangle area calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

The length of the base of the triangle

The perpendicular height from the base to the opposite vertex

Results

Area

30 sq units

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Triangle Area Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

The Triangle Area Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

Formula Reference

Triangle Area Calculator Formula

See calculator inputs for the governing equation

Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.

When to Use This Calculator

  • Use the Triangle Area Calculator when you need a quick mathematical result without writing out all the steps manually, saving time on repetitive calculations.
  • Use it to verify hand calculations on tests or assignments and catch arithmetic mistakes.
  • Use it when teaching or explaining mathematical concepts to others, demonstrating how changing inputs affects the result.
  • Use it to explore the behavior of mathematical functions across a range of inputs.

About This Calculator

The Triangle Area Calculator is a free mathematical calculation tool for students, educators, and professionals who need quick, reliable results. Calculate the area of a triangle using base and height. The classic formula A = ½ × base × height. The underlying algorithms implement well-established mathematical formulas and numerical methods. Results are computed instantly in the browser. This tool is useful for learning, verification of hand calculations, and rapid exploration of mathematical relationships. All computation happens locally — no data is sent to a server.

About Triangle Area Calculator

The triangle is one of the most fundamental shapes in geometry, and calculating its area is a skill used across mathematics, engineering, architecture, and science. A triangle is a polygon with three edges and three vertices. The simplest way to compute its area is with the formula A = ½ × base × height, where the height is the perpendicular distance from the chosen base to the opposite vertex. This formula works for all types of triangles — acute, right, and obtuse. Triangles are the building blocks of more complex polygons; any polygon can be divided into triangles, making triangle area a cornerstone concept. From surveying land parcels to designing roof trusses, this calculation appears constantly in practical applications. This calculator gives you the area instantly when you provide the base and height measurements.

The Math Behind It

The formula A = ½bh can be understood by observing that any triangle is exactly half of a parallelogram with the same base and height. If you duplicate a triangle and flip it, the two copies form a parallelogram with area b × h, so each triangle has area ½bh. This formula is valid regardless of which side you choose as the base, as long as you use the corresponding perpendicular height. For triangles where the height is difficult to measure directly, alternative formulas exist: Heron's formula uses all three side lengths, and the trigonometric formula A = ½ab sin(C) uses two sides and the included angle. The shoelace formula allows computing the area from vertex coordinates: A = ½|x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|. In calculus, triangle area connects to integration through the concept of Riemann sums, where areas under curves are approximated by sums of thin triangles or rectangles.

Formula Reference

Triangle Area

A = ½ × b × h

Variables: b = base, h = perpendicular height

Worked Examples

Example 1: Sail area

A triangular sail has a base of 8 m and a height of 12 m.

Step 1:A = ½ × 8 × 12
Step 2:A = ½ × 96

A = 48 square meters

Example 2: Road sign

A yield sign has a base of 36 inches and height of 31.2 inches.

Step 1:A = ½ × 36 × 31.2
Step 2:A = ½ × 1123.2

A = 561.6 square inches

Common Mistakes & Tips

  • !Using a slant side instead of the perpendicular height.
  • !Forgetting to multiply by ½, which gives the area of the full parallelogram instead.
  • !Confusing the altitude (height) with one of the sides of the triangle.

Related Concepts

Used in These Calculators

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Frequently Asked Questions

What if I do not know the height?

Use Heron's formula if you know all three sides, or use A = ½ab sin(C) if you know two sides and the included angle.

Does the formula work for obtuse triangles?

Yes. The height may fall outside the triangle for obtuse triangles, but the formula A = ½bh still applies when the perpendicular height is measured correctly.