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

Finance Formulas You'll Actually Use

These financial formulas appear regularly in personal finance, business, and investment decisions:

Compound Interest:

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

P = principal, r = annual rate (decimal), n = compounding periods/year, t = years. Example: €1,000 at 5% compounded monthly for 3 years: A = 1000 × (1 + 0.05/12)^36 = €1,161.62

Simple Interest:

I = P × r × t

€5,000 at 3% for 2 years: I = 5000 × 0.03 × 2 = €300 interest

Profit Margin:

Margin = (Revenue − Cost) ÷ Revenue × 100

Revenue €120, cost €80: margin = (120−80)/120 × 100 = 33.3%

Rule of 72 (investment doubling time):

Years to double ≈ 72 ÷ Annual Interest Rate

At 6% annual return: 72 ÷ 6 = 12 years to double your money.

Statistics Formulas for Everyday Data

Whether you're analysing survey results, comparing test scores, or reviewing business data, these statistical formulas are essential:

Mean (arithmetic average):

Mean = Σx ÷ n

Sum all values, divide by the count. The most common measure of central tendency.

Median:

The middle value when data is sorted in order. For an even number of values, average the two middle numbers. More robust than the mean when outliers are present.

Percentage change:

% Change = ((New − Old) ÷ Old) × 100

Price rose from €40 to €52: (52−40)/40 × 100 = 30% increase.

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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