Pythagorean theorem
$$a^2+b^2=c^2$$
Relate the legs and hypotenuse of a right triangle.
Middle school · High schoolGeometry formulas, grouped by topic.
30 geometry formulas across 7 topics, free and without an account. Geometry formulas convert a shape into a measurement. Area, perimeter, volume, and surface-area rules each assume something specific about the figure — a right angle, a perpendicular height, parallel bases, or a regular polygon — and using the slant side where the perpendicular height belongs is the single most common source of a wrong answer. Coordinate formulas extend the same measurements to the plane.
Every geometry formula on one page
Each entry links to its own page, where the symbols are defined, the conditions are stated, and the formula is substituted through a worked example. Levels covered here: Middle school, High school, University.
Triangles
5 formulas in triangles.
Triangle area
$$A=\frac12 bh$$
Find triangle area from a base and perpendicular height.
Middle schoolHeron’s formula
$$s=\frac{a+b+c}{2},\qquad A=\sqrt{s(s-a)(s-b)(s-c)}$$
Find triangle area from three side lengths.
High schoolTriangle angle sum
$$A+B+C=180^\circ=\pi\text{ radians}$$
Relate the three interior angles of a Euclidean triangle.
Middle schoolEquilateral triangle measures
$$h=\frac{\sqrt3}{2}s,\qquad A=\frac{\sqrt3}{4}s^2$$
Find the height and area of an equilateral triangle from one side.
Middle school · High schoolCoordinates
3 formulas in coordinates.
Distance in the plane
$$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$
Find straight-line distance between two coordinate points.
High schoolMidpoint
$$M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$$
Find the point halfway between two coordinate points.
High schoolDistance in three dimensions
$$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$$
Find straight-line distance between two points in three-dimensional Cartesian space.
High school · UniversityQuadrilaterals
3 formulas in quadrilaterals.
Rectangle area and perimeter
$$A=lw,\qquad P=2l+2w$$
Measure the interior and boundary of a rectangle.
Middle schoolParallelogram area
$$A=bh$$
Find area using one side as a base and its perpendicular height.
Middle schoolTrapezoid area
$$A=\frac12(b_1+b_2)h$$
Multiply height by the average of the parallel bases.
Middle schoolCircles
6 formulas in circles.
Circle circumference
$$C=2\pi r=\pi d$$
Measure the distance around a circle.
Middle schoolCircle area
$$A=\pi r^2$$
Measure the region enclosed by a circle.
Middle schoolCircle equation
$$(x-h)^2+(y-k)^2=r^2$$
Describe all points a fixed distance from a center.
High schoolArc length
$$s=r\theta$$
Find the length cut from a circle by a central angle.
High schoolSector area
$$A=\frac12r^2\theta$$
Find the area of a circular sector.
High schoolChord length
$$c=2r\sin\left(\frac{\theta}{2}\right)$$
Find the straight chord subtended by a central angle.
High schoolPolygons
4 formulas in polygons.
Interior-angle sum
$$S=(n-2)180^\circ$$
Add all interior angles of an $n$-sided polygon.
Middle school · High schoolRegular polygon area
$$A=\frac12aP=\frac{ns^2}{4\tan(\pi/n)}$$
Find area from apothem and perimeter or side count and side length.
High schoolExterior-angle sum
$$\sum \text{exterior angles}=360^\circ$$
Add one consistently directed exterior angle at every vertex of a polygon.
Middle school · High schoolRegular polygon angles
$$\text{interior angle}=\frac{(n-2)180^\circ}{n},\qquad \text{central angle}=\frac{360^\circ}{n}$$
Find equal interior and central angles of a regular polygon.
Middle school · High schoolSolids
8 formulas in solids.
Prism volume
$$V=Bh$$
Find volume from a constant base cross-section.
Middle schoolCylinder volume and surface area
$$V=\pi r^2h,\qquad S=2\pi r^2+2\pi rh$$
Measure a right circular cylinder’s volume and total exterior area.
Middle school · High schoolPyramid volume
$$V=\frac13Bh$$
Find a pyramid’s volume from base area and perpendicular height.
Middle schoolCone volume and surface area
$$V=\frac13\pi r^2h,\qquad S=\pi r^2+\pi r\ell$$
Measure a right circular cone’s volume and total surface area.
High schoolSphere volume and surface area
$$V=\frac43\pi r^3,\qquad S=4\pi r^2$$
Measure a sphere’s enclosed volume and outer area.
Middle school · High schoolRectangular prism volume and surface area
$$V=\ell wh,\qquad S=2(\ell w+\ell h+wh)$$
Measure the space inside and total exterior area of a rectangular prism.
Middle schoolCube volume and surface area
$$V=s^3,\qquad S=6s^2$$
Measure a cube using its common edge length.
Middle schoolPrism surface area
$$S=2B+Ph$$
Find the total area of two congruent bases and all lateral faces of a right prism.
Middle school · High schoolSimilarity
1 formula in similarity.
Similarity scale factors
$$\frac{L_2}{L_1}=k,\qquad\frac{A_2}{A_1}=k^2,\qquad\frac{V_2}{V_1}=k^3$$
Relate corresponding lengths, areas, and volumes of similar figures.
Middle school · High schoolKeep going with geometry
A formula sheet is a reference, not a method. Use the subject guide to see where these relationships come from, a calculator to check a substitution you are unsure about, and practice questions to find out whether you can actually retrieve them.
- Study geometry — the subject hub with lessons, worked methods, and common mistakes.
- Geometry calculator — enter your own values and compare the result with your working.
- Geometry Practice — retrieval practice across every topic listed above.
- Math formula library — search all 215 formulas by name, symbol, or condition.
Formulas in the other subjects
Mathematics does not stop at a subject boundary, and neither do its formulas. Each subject page below lists its own relationships, conditions, and worked examples.
Arithmetic
Review the core arithmetic relationships, their restrictions, and worked substitutions.
Algebra
Review the core algebra relationships, their restrictions, and worked substitutions.
Trigonometry
Review the core trigonometry relationships, their restrictions, and worked substitutions.
Precalculus
Review the core precalculus relationships, their restrictions, and worked substitutions.
Calculus
Review the core calculus relationships, their restrictions, and worked substitutions.
Statistics
Review the core statistics relationships, their restrictions, and worked substitutions.
Probability
Review the core probability relationships, their restrictions, and worked substitutions.
Linear Algebra
Review the core linear algebra relationships, their restrictions, and worked substitutions.
Differential Equations
Review the core differential equations relationships, their restrictions, and worked substitutions.
Discrete Math
Review the core discrete math relationships, their restrictions, and worked substitutions.