Math / Geometry

Geometry Solver

Solve triangles from SSS, SAS, ASA, AAS, or HL inputs, and calculate area and perimeter for circles, rectangles, trapezoids, squares, and triangles.

Triangle solverLaw of sines & cosinesArea & perimeterCongruence cases

Mode

Enter the known values for the selected case. All triangle angles are reported in degrees.

Known values

Three sides. The solver checks the triangle inequality and computes all angles via the law of cosines.

Results

Angle A

36.8699°

Angle B

53.1301°

Angle C

90°

Side A

3

Side B

4

Side C

5

Area

6

Perimeter

12

Need a change for Geometry Solver?

About this calculator

Method, formulas, and limits.

What this does

Solves the missing sides and angles of a triangle from the standard congruence cases (SSS, SAS, ASA, AAS, HL) and computes area and perimeter for common shapes.

Who it is for

Students, teachers, and anyone checking geometry homework, engineering sketches, or construction measurements.

How it works

The triangle solver applies the law of cosines, law of sines, and the angle-sum identity to the entered values, rejecting cases that violate the triangle inequality or angle rules.

Limitations

Inputs are treated as exact measurements. Results are rounded for display, and the tool does not handle ambiguous SSA cases or non-Euclidean geometry.

Key calculations

Law of cosines
c² = a² + b² − 2ab·cos(C)
Law of sines
a / sin(A) = b / sin(B) = c / sin(C)
Triangle inequality
a + b > c, a + c > b, and b + c > a must all hold.

How to use it

  1. 1.Pick a triangle caseChoose SSS, SAS, ASA, AAS, or HL and enter the known sides and angles in degrees.
  2. 2.Or pick a shapeSwitch to shape mode for area and perimeter of circles, rectangles, trapezoids, squares, or triangles.
  3. 3.Review the solved triangleAll three sides, all three angles, area, and perimeter are reported.
  4. 4.Check validityInputs that violate the triangle inequality or an angle-sum rule are rejected with an explanation.

SSS (three sides), SAS (two sides and the included angle), ASA (a side and its two adjacent angles), AAS (a side, an opposite angle, and another angle), and HL (hypotenuse and one leg of a right triangle).

The side lengths may violate the triangle inequality (a + b must exceed c), or the entered angles may not sum to less than 180 degrees.

Degrees. Enter the angles you have in degrees, and the solver reports all computed angles in degrees.

No. The ambiguous side-side-angle case is intentionally not supported because it can produce zero, one, or two valid triangles.

Triangle area uses Heron's formula after solving the triangle; circle, rectangle, trapezoid, and square use their standard formulas with the entered dimensions.

Related calculators

Quick jumps

Triangle Trigonometry Calculator

Solve right triangles with side lengths, angles, and trigonometry.

Open

Square Feet Calculator

Calculate area in square feet for rectangles, triangles, circles, and trapezoids. Use feet and inches together, trace on a map, then estimate tile, flooring, concrete, or paint.

Open

Square Root Simplifier

Simplify square roots into exact radical form and decimal form.

Open

Proportion Calculator

Solve a missing value in A:B = C:D with cross-multiplication steps and equivalence check.

Open