Essential Math Formulas Everyone Should Know
From calculating the area of a room to understanding interest rates, these foundational formulas show up constantly in everyday life, school, and work. Keep this reference handy.
Mathematics underlies almost every practical decision we make — from estimating how much paint to buy for a room to understanding whether a loan offer is fair. Most of these calculations rely on a surprisingly small set of formulas. This reference covers the most useful ones, with practical examples for each.
Percentages
- Part = (Percentage ÷ 100) × Whole — e.g. 20% of 350 = 0.20 × 350 = 70
- Percentage = (Part ÷ Whole) × 100 — e.g. 42 out of 60 = (42 ÷ 60) × 100 = 70%
- Percentage change = ((New − Old) ÷ Old) × 100
- To increase by X%: multiply by (1 + X/100)
- To decrease by X%: multiply by (1 − X/100)
Areas and Perimeters
- Rectangle: Area = length × width; Perimeter = 2(length + width)
- Triangle: Area = (base × height) ÷ 2
- Circle: Area = π × r²; Circumference = 2 × π × r (where r is radius)
- Trapezoid: Area = ½ × (a + b) × height (where a and b are parallel sides)
- Parallelogram: Area = base × height
Volumes
- Cube: Volume = side³
- Rectangular prism (box): Volume = length × width × height
- Cylinder: Volume = π × r² × height
- Sphere: Volume = (4/3) × π × r³
- Cone: Volume = (1/3) × π × r² × height
The Pythagorean Theorem
In a right-angled triangle: a² + b² = c², where c is the hypotenuse (longest side). This is used constantly in construction, navigation, and design. If you know two sides, you can always find the third: c = √(a² + b²). Common right-triangle combinations (Pythagorean triples) to recognise: 3-4-5, 5-12-13, 8-15-17.
Speed, Distance, and Time
- Distance = Speed × Time
- Speed = Distance ÷ Time
- Time = Distance ÷ Speed
Example: a car travels 300 km at 100 km/h. Time = 300 ÷ 100 = 3 hours. If the same journey takes 3.5 hours, average speed = 300 ÷ 3.5 = 85.7 km/h.
Interest and Finance
- Simple interest: I = P × r × t (P = principal, r = annual rate as decimal, t = years)
- Compound interest: A = P × (1 + r/n)^(n×t)
- Rule of 72: Years to double ≈ 72 ÷ annual interest rate
- Loan payment: EMI = P × [r(1+r)^n] ÷ [(1+r)^n − 1]
Statistics
- Mean (average): sum of all values ÷ number of values
- Median: the middle value when sorted; average of two middle values if even count
- Mode: the most frequently occurring value
- Range: maximum value − minimum value
- Variance: average of squared differences from the mean
- Standard deviation: square root of variance
Temperature Conversion
- °F to °C: (°F − 32) × 5/9
- °C to °F: (°C × 9/5) + 32
- °C to Kelvin: °C + 273.15
Useful Constants
- π (pi) ≈ 3.14159
- e (Euler's number) ≈ 2.71828
- √2 ≈ 1.41421
- √3 ≈ 1.73205
- Golden ratio (φ) ≈ 1.61803
Apply These Formulas Instantly
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