Introduction
This triangle side calculator finds the missing sides and angles of any triangle. Just enter three known values, like three sides, two angles and a side, or two sides and an angle, and the tool solves the rest. It uses the Law of Cosines and the Law of Sines to do the math for you.
The calculator handles every common case: SSS, SAS, ASA, AAS, and SSA (including the ambiguous case where two triangles are possible). You can also enter altitudes, medians, side ratios, or area to solve a triangle. Each result includes a step-by-step solution, a diagram, and a side length chart so you can see and check the work.
Choose between degrees or radians, set your decimal precision, and calculate one triangle or many at once. This tool gives you fast, accurate answers with full explanations.
How to Use Our Triangle Side Calculator
Enter any three known values of a triangle (sides, angles, or a mix of both) and this calculator will find all missing sides, angles, the perimeter, and a full step-by-step solution.
Side a, Side b, Side c: Type the length of any known side. Side a is across from Angle A, side b is across from Angle B, and side c is across from Angle C. Leave a field blank if you do not know it.
Angle A, Angle B, Angle C: Type the measure of any known angle. Angle A is the angle at vertex A, opposite side a. You need at least one side along with your angles to get a unique triangle.
Angle Unit: Pick Degrees or Radians to tell the calculator how to read your angle values. Most people use degrees. In radians mode you can type expressions like pi/2.
Decimal Precision: Choose how many decimal places to show in the results, from 0 to 5. Pick "Full" to see unrounded values.
Guided Fields vs. Freeform: Use the Guided Fields tab to type values into labeled boxes. Use the Freeform tab to type a quick expression like a=3 b=4 c=5. Freeform also accepts altitudes (ha, hb, hc), medians (ma, mb, mc), area (T), side ratios (a:b:c), and angle ratios (A:B:C).
Add Row: Click this button to add more triangle rows so you can solve several triangles at once in Guided mode.
Calculate: Press the Calculate button after you enter your values. The tool will show all six triangle values, a diagram, a side length comparison chart, and a detailed step-by-step solution.
How to Find the Missing Sides and Angles of a Triangle
A triangle is a shape with three straight sides and three angles. The three angles of any triangle always add up to 180 degrees. If you know at least three of a triangle's six measurements (three sides and three angles), and at least one of them is a side, you can figure out the rest. That is exactly what this triangle side calculator does.
The Rules Behind the Math
This calculator uses two main formulas from geometry to solve triangles:
- Law of Cosines: This formula connects all three sides of a triangle to one of its angles. It is used when you know three sides (SSS) or two sides and the angle between them (SAS).
- Law of Sines: This formula says that the ratio of a side to the sine of its opposite angle is the same for all three sides. It is used when you know two angles and a side (ASA or AAS), or two sides and an angle that is not between them (SSA).
What Is the Ambiguous Case?
When you know two sides and an angle that is not between those sides, something tricky can happen. There might be two different triangles that fit the same numbers. This is called the ambiguous case (SSA). The calculator checks for this and shows both answers when two valid triangles exist.
Triangle Types
Triangles are grouped by their sides and their angles:
- By sides: Equilateral (all three sides equal), Isosceles (two sides equal), or Scalene (no sides equal).
- By angles: Acute (all angles less than 90°), Right (one angle is exactly 90°), or Obtuse (one angle is greater than 90°).
Triangle Inequality Rule
Not every set of three numbers can be the sides of a triangle. The two shorter sides added together must be longer than the longest side. If they are not, no triangle can be formed. The calculator checks this rule automatically and tells you if your values are not valid.