Area of Triangle Calculator – Accurate & Instant

Find the area of any triangle in seconds with our Area of Triangle Calculator. Whether you know the base and height, three sides, or coordinates of vertices, this smart tool instantly computes the area using the right formula.

At Digital Calculator, we simplify geometry for students, teachers, architects, and professionals. With just a few inputs, our calculator delivers accurate results no manual computation or geometric memorization needed.

What Is the Area of a Triangle?

The area of a triangle is the amount of space enclosed within its three sides. It’s measured in square units (like cm², m², or ft²). The area depends on the shape and dimensions of the triangle — specifically, its sides, height, or angles.

Understanding how to find the area is essential in geometry, construction, architecture, and even in data visualization or design projects.

In essence, the area of a triangle represents half the area of a rectangle with the same base and height.

Mathematically:
Area = ½ × base × height

But that’s only one of several ways to find the area. Our Area of Triangle Calculator automatically applies the correct formula based on your given data.

Formulas to Find the Area of a Triangle

There are multiple formulas depending on what information you have. Let’s explore each one.

Using Base and Height

The most common formula:
Area = ½ × base × height

Where:

base = the length of the triangle’s bottom side
height = the perpendicular distance from the base to the opposite vertex

Example:

If base = 10 cm and height = 6 cm,

Area = ½ × 10 × 6 = 30 cm²

Answer: The area of the triangle is 30 cm²

Using Heron’s Formula (Three Sides Known)

When you know all three sides (a, b, c):

Find the semi-perimeter (s):
s = (a + b + c) / 2
Then apply:
Area = √[s × (s – a) × (s – b) × (s – c)]

Example:

Let sides be a = 5 cm, b = 6 cm, c = 7 cm.

s = (5 + 6 + 7) / 2 = 9
Area = √[9 × (9–5) × (9–6) × (9–7)]
Area = √[9 × 4 × 3 × 2] = √216 = 14.7 cm² (approx.)

Answer: The area is approximately 14.7 cm²

Our calculator handles all this complex calculation automatically you just enter the sides.

Using Coordinates of Vertices

If the vertices of a triangle are (x₁, y₁), (x₂, y₂), and (x₃, y₃):

Area = ½ × |x₁(y₂ – y₃) + x₂(y₃ – y₁) + x₃(y₁ – y₂)|

Example:

Points: (2, 4), (6, 8), (10, 2)

Area = ½ × |2(8–2) + 6(2–4) + 10(4–8)|

= ½ × |12 – 12 – 40| = ½ × 40 = 20 square units

Answer: The area is 20 square units

Using Trigonometric Formula (Two Sides and Included Angle)

When you know two sides and the angle between them (A):

Area = ½ × a × b × sin(C)

Example:

a = 8 cm, b = 10 cm, angle C = 30°

Area = ½ × 8 × 10 × sin(30°)

= ½ × 80 × 0.5 = 20 cm²

Answer: The area is 20 cm²

How to Use the Area of Triangle Calculator

Using our Free Area of Triangle Calculator is quick and straightforward:

Select a method — base & height, three sides, or coordinates.
Enter the values — fill in the required fields.
Click “Calculate.”
Instantly view your triangle’s area and relevant steps.

Try the Free Area of Triangle Calculator now on Digital Calculator and get instant, accurate results!

Step-by-Step Examples

Let’s see how the calculator simplifies different cases.

Example 1: Base and Height

Base = 12 cm, Height = 9 cm

Area = ½ × 12 × 9 = 54 cm²

Result: 54 cm²

Example 2: Three Sides (Heron’s Formula)

a = 7 cm, b = 9 cm, c = 10 cm
s = (7 + 9 + 10) / 2 = 13
Area = √[13 × (13–7) × (13–9) × (13–10)]
Area = √[13 × 6 × 4 × 3] = √936 = 30.6 cm²

Result: 30.6 cm²

Example 3: Two Sides and Angle

a = 5 cm, b = 8 cm, included angle = 45°
Area = ½ × 5 × 8 × sin(45°)
= 20 × 0.7071 = 14.14 cm²

Result: 14.14 cm²

Example 4: Using Coordinates

(1, 2), (4, 6), (5, 3)
Area = ½ × |1(6–3) + 4(3–2) + 5(2–6)|
= ½ × |3 + 4 – 20| = ½ × 13 = 6.5 square units

Result: 6.5 square units

Triangle Area Formula Summary Table

Known Parameters	Formula	Example Output
Base & Height	½ × base × height	½ × 10 × 6 = 30 cm²
Three Sides (a, b, c)	√[s(s–a)(s–b)(s–c)], where s = (a+b+c)/2	a=5, b=6, c=7 → 14.7 cm²
Coordinates	½ ×	x₁(y₂–y₃)+x₂(y₃–y₁)+x₃(y₁–y₂)
Two Sides & Angle	½ × a × b × sin(C)	a=8,b=10,C=30° → 20 cm²

Our calculator applies the right formula automatically giving you reliable, instant results for any triangle type.

Types of Triangles and Their Area

Triangle Type	Description	Example Formula
Equilateral	All sides equal	(√3 / 4) × side²
Isosceles	Two sides equal	½ × base × height
Scalene	All sides different	Use Heron’s formula
Right-angled	One 90° angle	½ × base × height

Our calculator supports all these triangle types automatically.

Applications of Triangle Area Calculation

The area of a triangle is used in countless real-world situations, including:

1. Construction & Architecture

Calculating roof areas, wall sections, or land plots that have triangular shapes.

2. Education

Students use triangle area formulas in geometry, trigonometry, and coordinate geometry problems.

3. Engineering

Engineers use triangle-based modeling for designing bridges, supports, and mechanical structures.

4. Design & Graphics

Graphic designers and data scientists use triangle area algorithms in image processing, meshes, and 3D modeling.

5. Everyday Measurements

DIY projects, landscaping, and home improvement tasks often rely on triangle area estimation.

No matter your purpose, our Free Area of Triangle Calculator helps you calculate quickly, precisely, and confidently.

Benefits of Using Digital Calculator Area of Triangle Tool

At Digital Calculator, we combine accuracy with ease of use. Here’s why our tool stands out:

Completely free to use — no sign-up required.
Multiple calculation methods — base-height, sides, coordinates, or angles.
Instant results — calculate in less than a second.
Educational breakdowns — learn while you calculate.
Error-free computations — powered by precise geometry logic.
Mobile-friendly design — works seamlessly on all devices.

Common Mistakes to Avoid

Even simple geometry can go wrong without care. Avoid these pitfalls:

Mixing up base and height — height must be perpendicular to the base.
Forgetting to halve the product in the base–height formula.
Using degrees incorrectly — always ensure your angle value is in degrees or radians consistently.
Entering side lengths that don’t form a valid triangle (violates the triangle inequality).