Math formulas for grades 5–11
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Short multiplication formulas
Short multiplication formulas let you expand and factor expressions without multiplying term by term: the square and cube of a sum or difference…
AlgebraEquations and Parabolas
A broad collection of algebra essentials: motion, work and cost problems, fractions and proportions, GCD and LCM, linear and quadratic equations…
GeometryTriangles
Everything about triangles in one place: the angle sum, exterior angle and triangle inequality, the Pythagorean theorem, the laws of sines and…
GeometryAreas of figures
Area formulas for rectangles, squares, parallelograms, rhombuses, triangles, trapezoids, regular polygons and more, often given in several…
GeometryPerimeters of figures
The perimeter is the total length of a figure's boundary.
GeometryTrapezoid
Area, perimeter, midsegment and height of a trapezoid, plus relations for the diagonals, the angles at a leg and the bases found from legs and angles.
GeometryCircle and Disk
Circumference, area, arcs, sectors and segments, chords, tangents and secants, and the equation of a circle — the formulas for circles, from the…
AlgebraSequences
Formulas for the nth term, the sum of the first n terms and the characteristic properties of arithmetic and geometric sequences, plus the sum of…
AlgebraCombinatorics
Permutations, arrangements and combinations, classical probability, the probability of a complementary event and of independent events…
AlgebraPowers and Logarithms
Rules for exponents, square roots and logarithms: multiplying and dividing powers, zero, negative and rational exponents, the definition and…
GeometryTrigonometry
Sine, cosine, tangent and cotangent of an acute angle, the fundamental identity, sum and double-angle formulas, the laws of sines and cosines…
GeometryTable of angle values
Reference tables of sine, cosine, tangent and cotangent for the standard angles 0°, 30°, 45°, 60°, 90°, 120°, 180°, 270° and 360°, plus the same…
AlgebraDerivatives and Integrals
A table of derivatives of power, exponential, logarithmic and trigonometric functions, the rules for differentiating sums, products, quotients and…
AlgebraAntiderivatives
Antiderivatives (indefinite integrals) of the most common functions: powers, 1/x, 1/√x, sine, cosine, eˣ and other exponentials, 1/cos²x and 1/sin²x.
GeometryVectors
Operations with vectors and coordinates in the plane and in space: sum and difference, length, dot product, the angle between vectors, the…
GeometryRectangular box and prism
Volume, surface area, the sum of the edge lengths and the space diagonal of a rectangular box, plus the volume and the lateral and total surface…
GeometrySolid geometry
Volumes and surface areas of the cube, rectangular box, prism, pyramid, cylinder, cone and sphere, along with diagonals, cross-sections and parts…
About this reference
Quantify is a free reference of 267 math formulas for students in grades 5–11: algebra, geometry, trigonometry, derivatives and integrals. Every formula comes with an explanation and notation, and most also have a diagram and a calculator. Pick a topic below, search by name, or print a cheat sheet in one click.