What is the most accurate method to calculate triangle area?

The accuracy depends on the information you have. For three known sides, Heron's formula is very accurate. For base and height, the simple formula (base × height) / 2 is most direct. Choose the method that matches your available data.

Can I calculate triangle area with only two sides?

No, you need at least three pieces of information to calculate triangle area. This could be three sides, two sides and an angle, two angles and a side, or base and height. Two sides alone are not sufficient.

What units can I use with the calculator?

The calculator supports meters, feet, yards, inches, centimeters, kilometers, and miles. All calculations are performed in the same unit system, and results are displayed in square units of your chosen measurement.

How do I know if my triangle is valid?

A triangle is valid if the sum of any two sides is greater than the third side. This is known as the triangle inequality theorem. Our calculator will show an error if you enter invalid side lengths.

What is Heron's formula and when should I use it?

Heron's formula calculates triangle area using only the three side lengths: Area = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2. Use it when you know all three sides but not the height.

Can I calculate the area of a right triangle differently?

Yes, for right triangles, you can use the formula (leg1 × leg2) / 2, which is simpler than Heron's formula. You can also use the Pythagorean theorem to find missing sides if needed.

What if I have coordinates instead of side lengths?

Use the coordinate method! Enter the (x,y) coordinates of all three vertices, and the calculator will use the shoelace formula to compute the area directly from the coordinates.

How precise are the calculations?

The calculator provides results with up to 6 decimal places for maximum precision. However, the actual precision depends on the accuracy of your input measurements.

Can I use this calculator for any type of triangle?

Yes, this calculator works for all types of triangles: acute, obtuse, right, equilateral, isosceles, and scalene. Choose the appropriate method based on the information you have.

What should I do if I get an error message?

Error messages usually indicate invalid input. Check that your side lengths satisfy the triangle inequality, angles are between 0-180°, and all required fields are filled with positive numbers.

🔺 Triangle Area Calculator

Free Triangle Area Calculator to find area using sides, base-height, angles, or coordinates. Quick, accurate, and easy tool for students and professionals.

Last updated: 2025-10-21 — Compiled and reviewed by Calvin (Math Research, FreeCalculators.app)

Three Sides (Heron's Formula)

Calculate area using Heron's formula when all three sides are known

Use Case:When you know all three side lengths

Wikipedia - Heron's Formula

Visualization

Formula

Area = sqrt[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2

Input Values

Side A (m)

Side B (m)

Side C (m)

Select Unit

Learn More About This Method

Get detailed explanations, formulas, use cases, and examples for this calculation method.

📚

View Detailed Guide

Base and Height

Calculate area using base and height (most common method)

Use Case:When you know the base and height

Khan Academy - Triangle Area

Visualization

Formula

Area = (Base x Height) / 2

Input Values

Base (m)

Height (m)

Select Unit

Learn More About This Method

Get detailed explanations, formulas, use cases, and examples for this calculation method.

📚

View Detailed Guide

Two Sides and Angle

Calculate area using two sides and the included angle

Use Case:When you know two sides and the angle between them

Math is Fun - Triangle Area with Trigonometry

Visualization

Formula

Area = (a x b x sin(C)) / 2

Input Values

Side 1 (m)

Side 2 (m)

Angle (degrees) (°)

Select Unit

Learn More About This Method

Get detailed explanations, formulas, use cases, and examples for this calculation method.

📚

View Detailed Guide

Two Angles and Side

Calculate area using two angles and one side

Use Case:When you know two angles and one side

Math Open Reference - Triangle Area

Visualization

∠C = 90°

Formula

Area = (a^2 x sin(B) x sin(C)) / (2 x sin(A))

Input Values

Angle 1 (degrees) (°)

Angle 2 (degrees) (°)

Side (m)

Select Unit

Learn More About This Method

Get detailed explanations, formulas, use cases, and examples for this calculation method.

📚

View Detailed Guide

Coordinate Method

Calculate area using three coordinate points

Use Case:When you have three coordinate points

Math Open Reference - Coordinate Triangle Area

Visualization

Formula

Area = |(x1(y2-y3) + x2(y3-y1) + x3(y1-y2)) / 2|

Input Values

Select Unit

Learn More About This Method

Get detailed explanations, formulas, use cases, and examples for this calculation method.

📚

View Detailed Guide

Right Triangle

Calculate area of a right triangle using two legs

Use Case:For right triangles when you know two legs

Khan Academy - Right Triangle Area

Visualization

Formula

Area = (Leg1 x Leg2) / 2

Input Values

Leg 1 (m)

Leg 2 (m)

Hypotenuse (m)

Select Unit

Learn More About This Method

Get detailed explanations, formulas, use cases, and examples for this calculation method.

📚

View Detailed Guide

A triangle area calculator is an essential tool for students, engineers, architects, and anyone working with geometric calculations. This comprehensive calculator supports multiple calculation methods, making it suitable for various scenarios where you need to find the area of a triangle with different given information.

Key Features

Our triangle area calculator offers comprehensive functionality for all your triangle area calculation needs.

✓Multiple calculation methods (6 different approaches)

✓Support for various units of measurement

✓Step-by-step calculation process

✓Visual triangle representation for three-sides method

✓Error handling for invalid inputs

✓Real-time calculation updates

✓Mobile-friendly responsive design

✓Privacy-focused with no data collection

Calculation Methods

Explore all six different methods to calculate triangle area. Each method is suitable for different scenarios based on the information you have.

Three Sides (Heron's Formula)

Wikipedia - Heron's Formula

Calculate area when you know all three side lengths. Uses Heron's formula which is perfect for any triangle. This method is ideal when you have measurements of all three sides but no height information.

Area = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2

Variables:

aLength of side A

bLength of side B

cLength of side C

Use Case:

When you have all three side lengths

Graphic Description:

Triangle with sides a, b, c labeled

Base and Height

Khan Academy - Triangle Area

The most common and straightforward method when you know the base length and the perpendicular height. This is the fundamental formula taught in elementary geometry.

Area = (Base × Height) / 2

Variables:

baseLength of the base

heightPerpendicular height from base to opposite vertex

Use Case:

When you have base and height measurements

Graphic Description:

Triangle with base and height perpendicular line shown

Two Sides and Included Angle

Math is Fun - Triangle Area with Trigonometry

Calculate area when you know two sides and the angle between them. This method uses trigonometry and is useful when height is difficult to measure directly.

Area = (a × b × sin(C)) / 2

Variables:

aLength of first side

bLength of second side

CAngle between the two sides (in degrees)

Use Case:

When you have two sides and the included angle

Graphic Description:

Triangle with two sides and the included angle marked

Two Angles and One Side

Math Open Reference - Triangle Area

Calculate area when you know two angles and one side length. This method uses the Law of Sines to find the missing sides, then calculates the area.

Area = (a² × sin(B) × sin(C)) / (2 × sin(A))

Variables:

aKnown side length

BFirst known angle (in degrees)

CSecond known angle (in degrees)

Use Case:

When you have two angles and one side

Graphic Description:

Triangle with two angles and one side marked

Coordinate Method

Math Open Reference - Coordinate Triangle Area

Calculate area using the coordinates of the three vertices. This method is perfect for triangles plotted on a coordinate plane or when working with GPS coordinates.

Area = |(x1(y2-y3) + x2(y3-y1) + x3(y1-y2)) / 2|

Variables:

(x1,y1)Coordinates of first vertex

(x2,y2)Coordinates of second vertex

(x3,y3)Coordinates of third vertex

Use Case:

When you have coordinates of all three vertices

Graphic Description:

Triangle plotted on coordinate plane with vertex coordinates

Right Triangle

Khan Academy - Right Triangle Area

Specialized calculation for right triangles using legs and hypotenuse. This is the simplest method for right triangles and uses the Pythagorean theorem.

Area = (Leg1 × Leg2) / 2

Variables:

leg1Length of first leg (perpendicular side)

leg2Length of second leg (perpendicular side)

Use Case:

When you have a right triangle with leg measurements

Graphic Description:

Right triangle with legs and right angle marked

How to Use the Triangle Area Calculator

Follow these simple steps to calculate triangle area using our comprehensive calculator.

1. Select Calculation Method

Choose the method that matches the information you have about your triangle. Options include three sides, base and height, two sides and angle, coordinates, and more.

2. Choose Units

Select your preferred unit of measurement from meters, feet, yards, inches, centimeters, kilometers, or miles.

3. Enter Values

Input the known values for your triangle. The required fields will change based on your selected calculation method.

4. View Results

The calculator will automatically compute the area and display the result along with the formula used and step-by-step calculations.

5. Visualize (Three Sides Method)

For the three sides method, you'll also see a visual representation of your triangle with labeled sides.

Tips for Accurate Calculations

Follow these tips to ensure accurate triangle area calculations.

1.Always double-check your input values for accuracy

2.Ensure angles are in degrees (0-180°) for angle-based calculations

3.For coordinate method, enter coordinates in the same unit system

4.Verify triangle validity - the sum of any two sides must be greater than the third side

5.Use appropriate precision for your measurements

6.For right triangles, ensure the Pythagorean theorem is satisfied

7.Check that angles sum to 180° for angle-based methods

8.Consider using the most appropriate method for your specific situation

Frequently Asked Questions

Common questions about triangle area calculations and our calculator.

Related Calculators

View all calculators →

⬜⚪

Area Calculator

Calculate the area of seven common shapes: rectangle, triangle, trapezoid, circle, sector, ellipse, and parallelogram. Perfect for geometry, construction, and land measurement.

Try it now

🔢

Basic Calculator

Perform essential math operations for daily calculations. Perfect for homework, budgeting, and quick calculations.

Try it now

📊

Percentage Calculator

Free percentage calculator. Quickly find percentage increase, decrease, change, or what percent of a number another number is. Easy & accurate.

Try it now