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Math Formulas Cheat Sheet: Frequently Used Calculations for Students and Professionals

Percentages, standard deviation, Pythagorean theorem, Fibonacci sequence, logarithms, and trigonometry — all the math formulas you need in one place, with instant calculators.

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.

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.

🌀 Fibonacci Calculator Compute the Nth Fibonacci number and golden ratio

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

📐 Trigonometry Calculator Get sin, cos, tan values for any angle

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

🎲 Combination & Permutation Calculator Quickly compute nCr and nPr

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

🔢 GCD & LCM Calculator Compute GCD and LCM using Euclidean algorithm

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.

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