SSS Triangle Calculator

Solve a triangle given its three sides (SSS) — computes all angles, area, perimeter, semi-perimeter.

Side a Side b Side c Select Unit

In triangle geometry, the SSS method stands for Side–Side–Side. This means you already know the lengths of all three sides of a triangle. Even though the sides are known, the angles, area, and other properties of the triangle may still be unknown.

The SSS Triangle Calculator helps you solve the entire triangle using only the three side lengths. It automatically calculates the interior angles, area, and perimeter using standard geometry formulas like the Law of Cosines and Heron’s Formula. This saves time, avoids mistakes, and makes triangle solving simple for students, teachers, engineers, and professionals.

What the SSS Triangle Calculator Is

A Three-Side Triangle Solver

The SSS Triangle Calculator is an online geometry tool designed to solve a triangle when all three sides are known. Unlike other triangle solvers that need angles, this calculator works only with side lengths.

You can use this calculator when you know:

Side a
Side b
Side c

With just these three values, the calculator finds all missing triangle properties.

What the Calculator Can Find

The calculator can determine:

All three interior angles
The area of the triangle
The perimeter
Triangle type (acute, right, or obtuse)

All results are based on standard trigonometry and geometry rules.

How the SSS Triangle Calculator Works

Step 1: Enter the Three Side Lengths

You begin by entering the values of sides a, b, and c.

Step 2: Apply the Law of Cosines

The calculator uses the Law of Cosines to find each angle.

Step 3: Apply Heron’s Formula

Once the angles are known, the calculator finds the area using Heron’s Formula.

Step 4: Display Full Triangle Solution

The calculator instantly shows angles, area, and perimeter.

This removes the need for manual trigonometry.

Key Formulas Used

Law of Cosines (Finding Angles)

To find angle A:

\cos(A) = \frac{b^2 + c^2 - a^2}{2bc}

A = \arccos!\left(\frac{b^2 + c^2 - a^2}{2bc}\right)

To find angle B:

B = \arccos!\left(\frac{a^2 + c^2 - b^2}{2ac}\right)

To find angle C:

C = \arccos!\left(\frac{a^2 + b^2 - c^2}{2ab}\right)

Heron’s Formula (Finding Area)

First find the semi-perimeter:

s = \frac{a + b + c}{2}

Then find the area:

\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}

Perimeter Formula

\text{Perimeter} = a + b + c

These formulas work for all triangle types.

Step-by-Step Example

Given Triangle Sides

a = 7 units
b = 9 units
c = 12 units

Step 1: Find Angle A

A = \arccos!\left(\frac{9^2 + 12^2 - 7^2}{2(9)(12)}\right)

A \approx 34.5^\circ

Step 2: Find Angle B

B = \arccos!\left(\frac{7^2 + 12^2 - 9^2}{2(7)(12)}\right)

B \approx 48.2^\circ

Step 3: Find Angle C

C = 180^\circ - (34.5^\circ + 48.2^\circ)

C \approx 97.3^\circ

Step 4: Find Area

s = \frac{7 + 9 + 12}{2} = 14

\text{Area} = \sqrt{14(14-7)(14-9)(14-12)}

\text{Area} \approx 27.8 \text{ square units}

The calculator performs all these steps instantly.

Features of the SSS Triangle Calculator

Solves Any Triangle Type

The calculator works for acute, right, and obtuse triangles.

Automatic Angle Calculation

Angles are found using the Law of Cosines.

Accurate Area Calculation

Heron’s Formula ensures precise area results.

Simple Input System

Only three side values are needed.

Uses and Applications

Education and Homework

Students use the calculator to solve triangle problems and check their answers quickly.

Engineering and Construction

Engineers use triangle solutions for structural planning and measurements.

Surveying and Design

Surveyors and designers use triangle properties for accurate layouts and mapping.

Tips to Avoid Common Mistakes

Many users enter side lengths that do not form a valid triangle. Always remember the triangle inequality rule: the sum of any two sides must be greater than the third side.

Another common mistake is forgetting that the Law of Cosines returns angles in degrees, not radians, in most calculators. Always check the angle unit.

Some users round numbers too early, which can cause inaccurate area results. Let the calculator complete all calculations before rounding.

Using inconsistent measurement units can also cause errors. Always keep all side lengths in the same unit system.

Finally, remember that Heron’s Formula requires the semi-perimeter value. If that is incorrect, the area result will also be wrong.

FAQs

What does SSS mean in triangles?

SSS means Side–Side–Side, where all three side lengths are known.

Can this calculator find angles?

Yes, it calculates all three angles.

Can it find the area?

Yes, it uses Heron’s Formula.

Does it work for all triangles?

Yes, as long as the side lengths form a valid triangle.

Final Words

The SSS Triangle Calculator is a powerful geometry tool that helps you solve a triangle completely using only three side lengths.

Whether you are a student, teacher, engineer, or designer, this calculator saves time, improves accuracy, and makes triangle geometry simple and reliable.