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 →4. Sequences: Fibonacci & Golden Ratio
The Fibonacci sequence appears everywhere — from sunflower spirals to stock market analysis.
Fibonacci
F(n) = F(n-1) + F(n-2), F(0)=0, F(1)=1
Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...
Golden Ratio
φ = (1 + √5) / 2 ≈ 1.6180339887...
The ratio of consecutive Fibonacci numbers converges to φ.
5. Logarithms & Trigonometry
Logarithms and trigonometric functions are indispensable tools in science, engineering, and computer science.
Logarithm
log_b(x) = y ⟺ b^y = x
Example: log₁₀(1000) = 3, because 10³ = 1000
Key properties: log(MN) = log(M)+log(N), log(M/N) = log(M)-log(N), log(M^k) = k·log(M).
📈 Logarithm Calculator Calculate logarithms with any base →Trigonometric Functions
sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, tan(θ) = opposite/adjacent
Example: sin(30°) = 0.5, cos(60°) = 0.5, tan(45°) = 1
6. Combinations & GCD/LCM
Combinations count how many ways you can choose items, while GCD and LCM solve problems involving divisibility and multiples.
Combination
C(n, r) = n! / (r! × (n-r)!)
Example: Choose 3 from 10 → C(10,3) = 120
GCD (Euclidean Algorithm)
GCD(a, b) = GCD(b, a mod b), stop when remainder = 0
Example: GCD(48,18) → GCD(18,12) → GCD(12,6) → GCD(6,0) = 6
LCM
LCM(a, b) = (a × b) / GCD(a, b)
Example: LCM(12,18) = 216/6 = 36
Wrap-Up
Math is not about memorization — it's about knowing which tool to use and when. Bookmark this page as your cheat sheet, and use CalKit's calculators whenever you need quick answers.