Math Reference Sheet

Quick reference for common formulas, conversions, and calculations. Bookmark this page or print for offline use.

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Percentages•Fractions•Geometry•Conversions•Algebra•Statistics

Percentage Quick Reference

Percentage ↔ Decimal ↔ Fraction

Percentage	Decimal	Fraction
10%	0.10	1/10
20%	0.20	1/5
25%	0.25	1/4
33.33%	0.333	1/3
50%	0.50	1/2
66.67%	0.667	2/3
75%	0.75	3/4

Percentage Formulas

What is X% of Y? → Y × (X/100)

X is what % of Y? → (X/Y) × 100

X is Y% of what? → X / (Y/100)

Percent Change: → [(New - Old) / Old] × 100

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Fraction Operations

Addition: a/b + c/d = (ad + bc) / bd

Subtraction: a/b - c/d = (ad - bc) / bd

Multiplication: a/b × c/d = ac / bd

Division: a/b ÷ c/d = ad / bc

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Geometry Formulas

2D Shapes

Shape	Area	Perimeter
Rectangle	l × w	2(l + w)
Square	s²	4s
Triangle	½ × b × h	a + b + c
Circle	πr²	2πr
Trapezoid	½(a + b) × h	a + b + c + d

3D Shapes

Shape	Volume	Surface Area
Cube	s³	6s²
Rectangular Prism	l × w × h	2(lw + lh + wh)
Sphere	(4/3)πr³	4πr²
Cylinder	πr²h	2πr² + 2πrh
Cone	(1/3)πr²h	πr² + πrl

Pythagorean Theorem

a² + b² = c²

For right triangles: the sum of squares of the two legs equals the square of the hypotenuse.

Common Unit Conversions

Length

1 inch = 2.54 cm

1 foot = 12 inches = 30.48 cm

1 yard = 3 feet = 0.9144 m

1 mile = 5,280 feet = 1.609 km

1 meter = 100 cm = 3.281 feet

1 kilometer = 1,000 m = 0.621 miles

1 cm = 10 mm = 0.394 inches

Weight/Mass

1 ounce = 28.35 grams

1 pound = 16 ounces = 453.6 g

1 ton (US) = 2,000 pounds

1 gram = 0.035 ounces

1 kilogram = 2.205 pounds

1 metric ton = 1,000 kg

Volume

1 cup = 8 fl oz = 236.6 mL

1 pint = 2 cups = 473 mL

1 quart = 2 pints = 946 mL

1 gallon = 4 quarts = 3.785 L

1 liter = 1,000 mL = 1.057 quarts

1 mL = 0.034 fl oz

1 cubic foot = 7.48 gallons

Temperature

Fahrenheit to Celsius: C = (F - 32) × 5/9

Celsius to Fahrenheit: F = C × 9/5 + 32

Celsius to Kelvin: K = C + 273.15

Algebra Essentials

Quadratic Formula

For ax² + bx + c = 0:

x = (-b ± √(b² - 4ac)) / 2a

Exponent Rules

x^a × x^b = x^a+b

x^a / x^b = x^a-b

(x^a)^b = x^ab

x⁰ = 1 (for x ≠ 0)

x^-a = 1/x^a

Logarithm Rules

log(xy) = log(x) + log(y)

log(x/y) = log(x) - log(y)

log(xⁿ) = n × log(x)

log_b(x) = log(x) / log(b)

Basic Statistics

Mean (Average): Sum of all values ÷ Number of values

Median: Middle value when sorted (or average of two middle values)

Mode: Most frequently occurring value

Range: Maximum value - Minimum value

Standard Deviation: √[Σ(x - mean)² / n]

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Mathematical Constants

Constant	Symbol	Value
Pi	π	3.14159265359...
Euler's Number	e	2.71828182846...
Golden Ratio	φ	1.61803398875...
Square Root of 2	√2	1.41421356237...