Perimeter and Area of a Triangle Calculator

Calculate triangle perimeter, area, missing sides, angles, heights, classifications, and coordinate results with clear formulas, unit conversions, validation, examples, and downloadable reports for everyone.

Calculation Results

Triangle Diagram

Formula Used

Step-by-Step Calculation

Unit Conversions

UnitPerimeterArea

Merged Result Data


            

Triangle Inputs

Three Side Lengths

Base, Height, and Optional Sides

Base and height calculate area. Enter all three sides to calculate perimeter and angles.

Two Sides and Included Angle

Right Triangle

Equilateral Triangle

Isosceles Triangle

Three Coordinate Points

Coordinate values use the selected input length unit.

Calculation History

DateModeTypePerimeterAreaUnit
No saved calculations.

Formula Used

Perimeter
P = a + b + c
Semiperimeter
s = (a + b + c) / 2
Base-height area
A = ½bh
Heron’s formula
A = √[s(s − a)(s − b)(s − c)]
SAS area
A = ½ab sin(C)
Equilateral area
A = (√3 / 4)a²

How to Use

Select the triangle calculation mode first. Enter every required value using one consistent length unit. Choose the required output precision before calculating.

Review the validity message and triangle classification. Check formulas, substitutions, angles, and converted measurements. Use the diagram to confirm the entered shape.

Copy results or download CSV and PDF reports. Saved history remains inside your browser. Clear it whenever stored calculations are unnecessary.

Example Data

ModeInputsExpected result
SSSa = 3, b = 4, c = 5Perimeter 12; area 6
Base and heightb = 10, h = 6Area 30
SASa = 8, b = 10, C = 60°Area about 34.641
Equilaterala = 9Perimeter 27; area about 35.074
CoordinatesA(0,0), B(6,0), C(2,5)Area 15

Frequently Asked Questions

How is a triangle perimeter calculated?

Add all three side lengths. The units remain linear. Every side must use the same unit.

How is triangle area calculated from base and height?

Multiply the base by perpendicular height. Divide that product by two. The result uses square units.

When should Heron’s formula be used?

Use it when all three sides are known. First calculate the semiperimeter. Then apply the square-root expression.

Can invalid sides form a triangle?

No side may equal or exceed the other two combined. This is the triangle inequality. Invalid inputs produce an error.

Can the calculator find missing sides?

Yes, selected modes find missing sides. SAS uses the cosine rule. Right triangles use the Pythagorean theorem.

How are triangle angles calculated?

The calculator uses inverse cosine relationships. All three sides must be available. Their angles should total 180 degrees.

What is a degenerate triangle?

Its points lie on one straight line. Its area equals zero. It is not a valid ordinary triangle.

Can coordinates calculate area?

Yes, the shoelace formula calculates coordinate area. Distance formulas calculate side lengths. Collinear points are rejected.

What is the difference between perimeter and area?

Perimeter measures the outer boundary length. Area measures the enclosed surface. Their units are therefore different.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.