Type any geometry problem into the box above and our geometry solver walks you through the full solution, one clear step at a time. From triangles and circles to area, angles, and volume, you will see exactly how each answer is found.
Free · Step-by-step worked solutions · Works on any device
What this geometry solver does
Our geometry solver takes a geometry problem written as text or built in the equation editor and returns a complete, step-by-step solution. Instead of just handing you a number, it shows the formula it used, the values it substituted, and the arithmetic in between, so you can follow the reasoning and learn the method.
It handles a wide range of topics, including:
- Triangles — side lengths with the Pythagorean theorem, missing angles, area, and perimeter.
- Circles — radius, diameter, circumference, area, and arc questions.
- Polygons — area and perimeter of rectangles, parallelograms, trapezoids, and regular shapes.
- Solid figures — surface area and volume of prisms, cylinders, cones, and spheres.
- Coordinate geometry — distance between points, midpoints, and slope.
Tip: include units and a clear goal
Write what you know and what you want to find, like “right triangle with legs 9 and 12, find the hypotenuse.” The clearer the setup, the cleaner the worked solution.
Worked examples
Example 1: Find the hypotenuse of a right triangle
A right triangle has legs of length \(9\) and \(12\). The Pythagorean theorem relates the legs \(a\) and \(b\) to the hypotenuse \(c\):
$$c = \sqrt{a^2 + b^2}$$Substitute \(a = 9\) and \(b = 12\):
$$c = \sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225} = 15$$Example 2: Find the missing angle in a triangle
The interior angles of any triangle add up to \(180^\circ\). Suppose two angles measure \(53^\circ\) and \(76^\circ\), and we want the third angle \(x\):
$$x = 180^\circ - 53^\circ - 76^\circ$$Work left to right:
$$x = 127^\circ - 76^\circ = 51^\circ$$Example 3: Find the area of a trapezoid
A trapezoid has parallel sides \(b_1 = 8\) and \(b_2 = 14\) with a height of \(h = 6\). The area formula is:
$$A = \tfrac{1}{2}\,(b_1 + b_2)\,h$$Substitute the values and simplify the bracket first:
$$A = \tfrac{1}{2}\,(8 + 14)(6) = \tfrac{1}{2}\,(22)(6) = \tfrac{1}{2}\,(132) = 66$$Common mistake
For a trapezoid, only the two parallel sides go inside the bracket, and \(h\) must be the perpendicular height — not a slanted side. Mixing these up is the most frequent error in area questions.
How to use the geometry solver
- Enter your problem. Type it into the box or use the equation editor to add symbols like \(\pi\), square roots, and exponents.
- Run the solver. Our AI engine reads the problem, picks the right formula, and lays out each step clearly.
- Review and learn. Read through the substitution and arithmetic, then check your own work or try a similar problem to lock in the method.
Key formulas to remember
Circle area \(A = \pi r^2\), circle circumference \(C = 2\pi r\), triangle area \(A = \tfrac{1}{2}bh\), and the angle sum of a triangle \(= 180^\circ\). Keeping these handy makes most problems faster to set up.
Related step-by-step guides
- How to Use the Pythagorean Theorem — find missing sides in right triangles with confidence.
- How to Find the Area of Any Shape — formulas for triangles, circles, and polygons in one place.
- How to Calculate Angles in a Triangle — use the angle sum and exterior angles to solve for unknowns.
- Surface Area and Volume Formulas Explained — work with prisms, cylinders, cones, and spheres.
Keep solving with our other tools
Geometry often leads into algebra, so when an equation pops up try our Equation Solver or the broader Algebra Solver for the same kind of step-by-step help.
