Math Formulas Reference | MathSite Education

🔢 Arithmetic Formulas

Basic arithmetic operations and properties fundamental to mathematics education.

Addition

a + b = c

Sum of two numbers

Commutative: a + b = b + a

Associative: (a + b) + c = a + (b + c)

Subtraction

a - b = c

Difference between two numbers

Not Commutative: a - b ≠ b - a

Not Associative: (a - b) - c ≠ a - (b - c)

Multiplication

a × b = c

Product of two numbers

Commutative: a × b = b × a

Associative: (a × b) × c = a × (b × c)

Distributive: a × (b + c) = a×b + a×c

Division

a ÷ b = c

Quotient of two numbers

Not Commutative: a ÷ b ≠ b ÷ a

Division by zero: Undefined

Order of Operations

PEMDAS/BODMAS

Parentheses, Exponents, Multiplication/Division, Addition/Subtraction

Average (Mean)

Mean = (Sum of values) ÷ (Number of values)

The arithmetic average of a set of numbers

📏 Geometry Formulas

Essential geometric formulas for calculating area, perimeter, and volume in mathematics education.

Square Area

A = s²

Area of a square with side length s

Example: s = 5, A = 25

Square Perimeter

P = 4s

Perimeter of a square with side length s

Rectangle Area

A = l × w

Area of rectangle with length l and width w

Rectangle Perimeter

P = 2(l + w)

Perimeter of rectangle

Triangle Area

A = ½ × b × h

Area of triangle with base b and height h

Triangle Perimeter

P = a + b + c

Perimeter of triangle with sides a, b, c

Pythagorean Theorem

a² + b² = c²

For right triangles, where c is the hypotenuse

Circle Area

A = πr²

Area of circle with radius r

Circumference

C = 2πr or C = πd

Circumference of circle with radius r or diameter d

Trapezoid Area

A = ½(a + b)h

Area of trapezoid with parallel sides a and b

Parallelogram Area

A = b × h

Area of parallelogram with base b and height h

Circle Sector Area

A = ½r²θ

Area of sector with radius r and angle θ (in radians)

📦 Volume Formulas

Formulas for calculating the volume of three-dimensional shapes in mathematics education.

Cube Volume

V = s³

Volume of cube with side length s

Rectangular Prism

V = l × w × h

Volume of rectangular prism

Sphere Volume

V = (4/3)πr³

Volume of sphere with radius r

Cylinder Volume

V = πr²h

Volume of cylinder with radius r and height h

Cone Volume

V = (1/3)πr²h

Volume of cone with radius r and height h

Pyramid Volume

V = (1/3) × Base Area × h

Volume of pyramid with height h

Triangular Prism

V = (½ × b × h) × l

Volume of triangular prism

Hemisphere Volume

V = (2/3)πr³

Volume of hemisphere

🔤 Algebra Formulas

Fundamental algebraic formulas and identities for mathematics education.

Quadratic Formula

x = (-b ± √(b² - 4ac)) / 2a

Solves ax² + bx + c = 0

Perfect Square (a+b)²

(a + b)² = a² + 2ab + b²

Square of a binomial sum

Perfect Square (a-b)²

(a - b)² = a² - 2ab + b²

Square of a binomial difference

Difference of Squares

a² - b² = (a + b)(a - b)

Factoring difference of squares

Sum of Cubes

a³ + b³ = (a + b)(a² - ab + b²)

Factoring sum of cubes

Difference of Cubes

a³ - b³ = (a - b)(a² + ab + b²)

Factoring difference of cubes

Exponent Rules

aᵐ × aⁿ = aᵐ⁺ⁿ

aᵐ ÷ aⁿ = aᵐ⁻ⁿ

(aᵐ)ⁿ = aᵐⁿ

Laws of exponents

Slope Formula

m = (y₂ - y₁) / (x₂ - x₁)

Slope between two points

Distance Formula

d = √[(x₂-x₁)² + (y₂-y₁)²]

Distance between two points

Midpoint Formula

M = ((x₁+x₂)/2, (y₁+y₂)/2)

Midpoint between two points

Slope-Intercept Form

y = mx + b

Linear equation with slope m and y-intercept b

Point-Slope Form

y - y₁ = m(x - x₁)

Line through point (x₁, y₁) with slope m

💯 Percentage Formulas

Essential percentage calculations for practical mathematics education.

Percentage

P% = (Part / Whole) × 100

Calculate percentage

Percentage of Number

Part = (P% × Whole) / 100

Find P% of a number

Percentage Increase

% Increase = ((New - Old) / Old) × 100

Calculate percentage increase

Percentage Decrease

% Decrease = ((Old - New) / Old) × 100

Calculate percentage decrease

Discount

Sale Price = Original × (1 - Discount%)

Calculate discounted price

Tax Calculation

Total = Price × (1 + Tax%)

Calculate price with tax

📊 Statistics Formulas

Basic statistical formulas for data analysis in mathematics education.

Mean (Average)

x̄ = Σx / n

Sum of values divided by count

Median

Middle value when sorted

For odd n: position (n+1)/2

For even n: average of two middle values

Mode

Most frequent value

Value that appears most often

Range

Range = Maximum - Minimum

Spread of data values

Variance

σ² = Σ(x - x̄)² / n

Measure of data spread

Standard Deviation

σ = √(Variance)

Square root of variance

Probability

P(A) = Favorable / Total

Probability of event A occurring

Combinations

C(n,r) = n! / [r!(n-r)!]

Number of ways to choose r items from n

Permutations

P(n,r) = n! / (n-r)!

Number of ways to arrange r items from n

📐 Trigonometry Formulas

Basic trigonometric ratios and identities for mathematics education.

Sine

sin θ = Opposite / Hypotenuse

Ratio in right triangle

Cosine

cos θ = Adjacent / Hypotenuse

Ratio in right triangle

Tangent

tan θ = Opposite / Adjacent

Ratio in right triangle

Pythagorean Identity

sin²θ + cos²θ = 1

Fundamental identity

Law of Sines

a/sin A = b/sin B = c/sin C

For any triangle

Law of Cosines

c² = a² + b² - 2ab cos C

For any triangle

Quick Reference Constants

Pi (π)

3.14159...

Euler's Number (e)

2.71828...

Golden Ratio (φ)

1.61803...

Speed of Light (c)

299,792,458 m/s