Type a geometry problem or upload a photo of the diagram and follow the working line by line, with the theorem named at every step.
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This free AI geometry solver works through triangles, circles, polygons, area, surface area, volume, coordinate geometry and proofs one line at a time. Type the problem, paste it, or upload a photo of the diagram.
Geometry is the subject where the answer on its own is worth the least. A length of 10 tells you nothing about why the Pythagorean theorem applied, which sides were the legs, or whether the triangle had to be right-angled in the first place. Every step here names the theorem or formula being used and shows the substitution that follows from it.
That makes the working checkable. Hold it next to your own solution, find the first line where the two differ, and ask a follow-up about that step on its own rather than starting the problem over.
The theorem is named before the arithmetic starts.
The formulas most geometry homework turns on, each with one substitution worked through so you can see where the numbers go.
Area = (1/2) x base x height. Pythagorean theorem: a^2 + b^2 = c^2 for a right triangle. With legs 6 and 8, c^2 = 36 + 64 = 100, so c = 10 and the area is (1/2)(6)(8) = 24. The three interior angles always sum to 180 degrees, which is what lets you find a missing angle from the other two.
Circumference = 2 x pi x r, area = pi x r^2. With r = 7, the circumference is 14pi (about 43.98) and the area is 49pi (about 153.94). Arc length and sector area are the same formulas scaled by the fraction of the full turn the angle covers.
Rectangle area = length x width; parallelogram area = base x height; trapezoid area = (1/2)(b1 + b2)h. The interior angles of an n-sided polygon sum to (n - 2) x 180 degrees. For a hexagon that is (6 - 2) x 180 = 720 degrees, so a regular hexagon has interior angles of 120 degrees each.
Cylinder volume = pi r^2 h, surface area = 2 pi r^2 + 2 pi r h. Sphere volume = (4/3) pi r^3, surface area = 4 pi r^2. Cone volume = (1/3) pi r^2 h. With r = 3 and h = 10, the cylinder holds 90pi (about 282.74) cubic units and its surface area is 18pi + 60pi = 78pi (about 245.04) square units.
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2). Midpoint = ((x1 + x2)/2, (y1 + y2)/2). Slope = (y2 - y1) / (x2 - x1). For (1, 2) and (4, 6) the distance is sqrt(9 + 16) = 5, the midpoint is (2.5, 4) and the slope is 4/3.
Once the geometry turns into an equation to rearrange, the AI algebra solver takes it from there; optimisation and rate-of-change problems built on a figure belong to the AI calculus solver.
Upload a photo of the figure and the question together. The solver reads the labelled sides, angles and markings from the diagram, states which theorem or formula applies, and works through the calculation step by step. Handwritten constructions and scanned worksheets work the same way. If you drew the figure yourself, include the given values in the image or type them alongside.
Geometry is the subject where this matters most, because half the information usually lives in the drawing rather than the sentence — the tick marks showing two sides are equal, the square in the corner showing a right angle, the arc marking an angle as congruent.
When a value the problem needs is missing from the image, the solver asks for it rather than assuming a number — a guessed side length quietly invalidates every line that follows.
The four groups most geometry courses are built from, whether you are in a high-school geometry class or an introductory college course.
Triangles, congruence and similarity, circles, quadrilaterals and polygons, angle relationships. That includes the angle rules that do most of the work in early problems: vertical angles, the angles formed when a transversal crosses parallel lines, and the exterior angle of a triangle.
Perimeter, area, surface area and volume for 2D and 3D figures. Composite shapes are split into pieces whose formulas you already know, and units are carried through the calculation so a volume comes out in cubic units rather than as a bare number.
Distance, midpoint, slope, equations of lines and circles, transformations. Proving a quadrilateral is a parallelogram from its four vertices, or showing two lines are perpendicular because their slopes multiply to -1, are the coordinate versions of classic plane-geometry proofs.
Right-triangle trig, law of sines and cosines, two-column and paragraph proofs. Sine, cosine and tangent find a missing side or angle in a right triangle; the law of sines and the law of cosines extend that to triangles with no right angle at all.
A proof is the part of geometry that a calculator cannot help with, because the answer is the reasoning. The solver lays out the statements and the reasons in order and names the theorem, postulate or definition that justifies each line.
Take the parallelogram proof: the diagonals bisect each other because the two triangles they cut are congruent by ASA — alternate interior angles give two pairs of equal angles, the opposite sides are equal, and corresponding parts of congruent triangles are congruent. Each of those four steps is a line with a reason next to it, which is exactly the form the assignment asks for.
An answer that disagrees with yours tells you only that something went wrong, not where. Paste or photograph your own working next to the problem and ask where the two solutions diverge.
In geometry the divergence is usually one of a handful of things: the wrong side taken as the hypotenuse, a radius used where the formula wanted a diameter, degrees mixed with radians, or an area formula applied to a figure whose height is not the side length. The solver traces your steps against its own and points at the first line that differs.
Area of the circle = pi x 14^2
Area of the circle = pi x 7^2
The first line where the two solutions differ.
Most searches for geometry help happen late, with a worksheet of figures and a deadline in the morning. A solver that is awake then is worth more than one that is thorough on Monday.
Work a problem set through one question at a time, ask for the same figure explained a different way, or have the solver generate extra practice on whichever topic keeps costing you marks — circle theorems one week, volume of composite solids the next. Follow-ups stay in the same chat, so the figure does not have to be described again.
Working through a specific calculation? These free tools solve one step at a time and show the working, so you can check each number against your own.
Every one of these shows the intermediate values, not just the result — the same reason the geometry solver writes the steps out.
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What is the area of a triangle with base 10 cm and height 6 cm?
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