Math formulas are essential not just for students, but also for professionals, developers, and data analysts. Here we compile the most frequently used math formulas in one place, with CalKit calculators so you can compute instantly.
This guide covers percentages, statistics, geometry, sequences, logarithms, and combinatorics — six areas of math you will encounter in everyday life and work.
📑 Table of Contents
1. Percentages and Ratios
Percentages are the most commonly used math concept in daily life — from discounts and grades to revenue growth and tips.
Formula
Percentage(%) = (Part / Whole) × 100
Example: 20 out of 80 passed → (20/80) × 100 = 25%
Percent Change
Change(%) = ((New - Old) / Old) × 100
Example: Revenue from $5,000 to $6,500 → ((6500-5000)/5000) × 100 = 30%
Common mistake: A 20% increase followed by a 20% decrease does NOT return to the original value. 100 → 120 → 96.
📐 Percentage Calculator Calculate percentages instantly →2. Statistics: Standard Deviation & Mean
The mean tells you the center of data; the standard deviation tells you how spread out it is. Both are fundamental for anyone working with data.
Mean
x̄ = (x₁ + x₂ + ... + xₙ) / n
Example: Scores 85, 90, 78, 92, 88 → mean = 86.6
Standard Deviation
σ = √( Σ(xᵢ - x̄)² / n )
Population uses n; sample standard deviation (s) uses n-1.
68-95-99.7 Rule: In a normal distribution, about 68% of data falls within ±1σ, 95% within ±2σ, and 99.7% within ±3σ of the mean.
📊 Standard Deviation Calculator Enter data to get mean, variance, and standard deviation →3. Geometry: Pythagorean Theorem
One of the most famous formulas in mathematics, still used daily in construction, navigation, game development, and more.
Formula
a² + b² = c² (c = hypotenuse)
Example: a=3, b=4 → c = √(9+16) = 5
Pythagorean Triples: (3,4,5), (5,12,13), (8,15,17), (7,24,25) — integer right triangles useful for quick mental math.
📐 Pythagorean Theorem Calculator Find the missing side of a right triangle →