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Mathematical Formulas Reference

Comprehensive collection of mathematical formulas with detailed explanations, examples, and real-world applications across all major fields of mathematics.

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x²

Algebra

Essential algebraic formulas including quadratic equations, logarithms, and polynomial expressions.
△

Geometry

Area, volume, and perimeter formulas for 2D and 3D shapes.
sin

Trigonometry

Trigonometric functions, identities, and laws for angles and triangles.
∫

Calculus

Derivatives, integrals, limits, and series formulas.
σ

Statistics

Statistical measures, probability distributions, and data analysis formulas.
F

Physics

Fundamental physics formulas for mechanics, energy, waves, and more.

Featured Formulas

algebra

Quadratic Formula

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Solves quadratic equations of the form ax² + bx + c = 0.
algebra

Slope Formula

m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}

Calculates the slope of a line between two points.
algebra

Distance Formula

d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}

Finds the distance between two points in a coordinate plane.
geometry

Pythagorean Theorem

a2+b2=c2a^2 + b^2 = c^2

In a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides.
geometry

Circle Area

A=πr2A = \pi r^2

Calculates the area of a circle given its radius.
trigonometry

Sine Definition

sin⁡θ=oppositehypotenuse\sin\theta = \frac{opposite}{hypotenuse}

Basic sine ratio in a right triangle.