Essential Math Formulas Everyone Should Know

Math formulas are the building blocks of countless everyday calculations. Whether you're calculating a tip, measuring a room for new flooring, or managing your budget, having these essential formulas at your fingertips makes life easier. This comprehensive guide covers the most useful formulas you'll encounter in daily life.

Percentage Formulas

Percentages are everywhere — discounts, taxes, tips, and more. Master these formulas:

Finding X% of a number:

Result = Number × (Percentage ÷ 100)

Example: 15% of 80 = 80 × 0.15 = 12

Percentage increase:

New Value = Original × (1 + Percentage ÷ 100)

Example: 80 increased by 15% = 80 × 1.15 = 92

Percentage decrease:

New Value = Original × (1 - Percentage ÷ 100)

Example: 80 decreased by 15% = 80 × 0.85 = 68

What percentage is X of Y:

Percentage = (X ÷ Y) × 100

Example: What % is 24 of 80? = (24 ÷ 80) × 100 = 30%

Geometry Formulas

Area Formulas

Shape	Formula	Variables
Rectangle	A = l × w	l = length, w = width
Square	A = s²	s = side
Triangle	A = ½ × b × h	b = base, h = height
Circle	A = π × r²	r = radius
Trapezoid	A = ½ × (a + b) × h	a, b = parallel sides, h = height

Perimeter and Circumference

Rectangle: P = 2l + 2w or P = 2(l + w)

Square: P = 4s

Triangle: P = a + b + c (sum of all sides)

Circle (Circumference): C = 2πr or C = πd

Volume Formulas

Rectangular Box: V = l × w × h

Cube: V = s³

Cylinder: V = πr²h

Sphere: V = (4/3)πr³

Cone: V = (1/3)πr²h

Financial Formulas

Simple Interest:

I = P × r × t

P = principal, r = rate (decimal), t = time in years

Compound Interest:

A = P(1 + r/n)^(nt)

n = compounding frequency per year

Profit Margin:

Margin = ((Revenue - Cost) ÷ Revenue) × 100

Break-Even Point:

Units = Fixed Costs ÷ (Price per Unit - Variable Cost per Unit)

Speed, Distance, and Time

These three formulas are interrelated and incredibly useful for travel planning:

Distance: d = s × t

Speed: s = d ÷ t

Time: t = d ÷ s

Example: If you travel at 60 km/h for 2.5 hours, you cover 60 × 2.5 = 150 km.

Temperature Conversion

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

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

Celsius to Kelvin: K = °C + 273.15

Pythagorean Theorem

For right triangles, this formula relates the sides:

a² + b² = c²

Where c is the hypotenuse (longest side) and a, b are the other two sides.

Practical use: Find the diagonal of a rectangle with sides 3m and 4m:

c = √(3² + 4²) = √(9 + 16) = √25 = 5m

Average (Mean)

Average = Sum of all values ÷ Number of values

Example: Average of 85, 90, 78, 92 = (85+90+78+92) ÷ 4 = 345 ÷ 4 = 86.25

Quick Reference Card

Everyday Calculations

Tip (15%): Total × 0.15
Tip (20%): Total × 0.20
Sales tax: Price × (1 + tax rate)
Discount: Price × (1 - discount %)

Useful Constants

π (pi) ≈ 3.14159
e ≈ 2.71828
√2 ≈ 1.41421
1 mile ≈ 1.609 km

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