Formula Reference Library

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79 Formulas✓ Free to use✓ With examples

📐79 Formulas

📂11 Categories

✅Free to use

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Math Formulas

13

Percentage Formula — How to Calculate Percentage

Percentage (%) = (Part ÷ Whole) × 100

Percentage Increase Formula — Step-by-Step Guide

% Increase = ((New Value − Original Value) ÷ Original Value) × 100

Pythagorean Theorem Formula — a² + b² = c² Explained

a² + b² = c²

Area Formula — Shapes: Square, Rectangle, Circle, Triangle

Square: A = s²

Volume Formula — Cube, Sphere, Cylinder, Cone

Cube: V = s³

Speed, Distance, Time Formula Explained

Distance = Speed × Time

Quadratic Formula — x = (−b ± √(b²−4ac)) / 2a

x = (−b ± √(b² − 4ac)) ÷ (2a)

Circle Area Formula — A = πr²

A = π × r²

Triangle Area Formula — ½ × Base × Height

A = ½ × b × h

Rectangle Area Formula — Length × Width Explained

Surface Area Formula — Sphere, Cylinder, Cube & More

Sphere: SA = 4πr²
Cylinder: SA = 2πr(h + r)
Cube: SA = 6s²
Rectangular Prism: SA = 2(lw + lh + wh)
Cone: SA = πr(r + l)

Perimeter Formula — Rectangle, Triangle, Circle & More

Rectangle: P = 2(L + W)
Square: P = 4s
Triangle: P = a + b + c
Circle (Circumference): C = 2πr = πd
Regular Polygon: P = n × s

GPA Formula — Weighted Grade Point Average

GPA = Σ(Grade Points × Credits) / Σ(Credits)

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Finance Formulas

20

Compound Interest Formula — Explained with Examples

A = P × (1 + r/n)^(nt)

Mortgage Payment Formula — Monthly Payment Calculation

M = P × [r(1+r)^n] ÷ [(1+r)^n − 1]

ROI Formula — Return on Investment Calculation

ROI (%) = ((Net Profit ÷ Cost of Investment) × 100

Discount Formula — How to Calculate Sale Price

Sale Price = Original Price × (1 − Discount% ÷ 100)

Sales Tax Formula — How to Calculate Tax on a Purchase

Tax Amount = Price × (Tax Rate ÷ 100)

Loan Payment Formula — Calculate Monthly Payments

M = P × [r(1+r)^n] ÷ [(1+r)^n − 1]

VAT Formula — How to Calculate Value Added Tax

Price incl. VAT = Net Price × (1 + VAT Rate ÷ 100)

CAGR Formula — Compound Annual Growth Rate Explained

CAGR = (End Value ÷ Start Value)^(1 ÷ n) − 1

Savings Formula — Future Value of Regular Deposits

FV = PMT × [(1 + r)^n − 1] ÷ r

Tip Formula — How to Calculate a Restaurant Tip

Tip Amount = Bill × (Tip % ÷ 100)

Inflation Formula — How to Calculate Real Value Over Time

Future Value = Present Value × (1 + Inflation Rate)^Years

Simple Interest Formula — I = PRT Explained

I = P × R × T

Net Worth Formula — Assets Minus Liabilities

Net Worth = Total Assets − Total Liabilities

Loan-to-Value (LTV) Ratio Formula

LTV = (Loan Amount ÷ Property Value) × 100

Debt-to-Income Ratio Formula — DTI Calculation

DTI = (Total Monthly Debt Payments ÷ Gross Monthly Income) × 100

Net Present Value (NPV) Formula

NPV = Σ[Cₜ ÷ (1+r)ᵗ] − C₀

Credit Card Interest Formula (Daily Periodic Rate)

Interest = Average Daily Balance × (APR / 365) × Days in Cycle

Savings PMT Formula — Monthly Contribution Goal

PMT = FV × (r/n) / [(1 + r/n)^(n×t) − 1]

Take-Home Pay Formula (Net Salary)

Net = Gross − Pre-Tax − FICA − Federal − State − Post-Tax

Salary ↔ Hourly Conversion Formula

Hourly = Annual / 2080 · Annual = Hourly × 2080

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Health Formulas

12

BMI Formula — Body Mass Index Calculation Explained

BMI = Weight (kg) ÷ Height (m)²

BMR Formula — Basal Metabolic Rate Calculation

BMR = (10 × weight_kg) + (6.25 × height_cm) − (5 × age) + 5

Calorie Burn Formula — How to Calculate Calories Burned

Calories Burned = MET × Weight (kg) × Time (hours)

Ideal Weight Formula — How to Calculate Your Ideal Body Weight

Men: 48 kg + 2.7 kg per inch over 5 feet

Calorie Formula — BMR and TDEE Calculation

Men: BMR = 10W + 6.25H − 5A + 5
Women: BMR = 10W + 6.25H − 5A − 161

Waist-to-Hip Ratio Formula — Health Risk Assessment

WHR = Waist Circumference ÷ Hip Circumference

Target Heart Rate Formula

Max HR = 220 − age
Fat Burn Zone: 50–70% of Max HR
Cardio Zone: 70–85% of Max HR
Peak Zone: 85–95% of Max HR

TDEE Formula — Total Daily Energy Expenditure

TDEE = BMR × Activity Multiplier

Mifflin-St Jeor BMR:
Men: BMR = (10×W) + (6.25×H) − (5×A) + 5
Women: BMR = (10×W) + (6.25×H) − (5×A) − 161

Calorie Deficit Formula — How to Calculate for Weight Loss

Daily Deficit = TDEE − Daily Calorie Intake
Weekly Weight Loss = (Daily Deficit × 7) / 7,700

1 kg fat ≈ 7,700 kcal
1 lb fat ≈ 3,500 kcal

Body Fat Percentage Formula — US Navy & BMI Methods

Men: BF% = 86.010 × log₁₀(waist − neck) − 70.041 × log₁₀(height) + 36.76
Women: BF% = 163.205 × log₁₀(waist + hip − neck) − 97.684 × log₁₀(height) − 78.387

Macros Formula — Protein, Carbs & Fat Targets

Carbs (g) = (Total kcal − Protein g × 4 − Fat g × 9) ÷ 4

Running Pace Formula — min/mile & min/km

Pace = Total Time / Total Distance

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Statistics Formulas

7

Standard Deviation Formula — Population & Sample

σ = √[ Σ(xᵢ − μ)² ÷ N ]

Z-Score Formula — Standard Score Calculation

z = (x − μ) ÷ σ

Mean Formula — How to Calculate the Average

Mean (x̄) = Σxᵢ / n (Sum of all values divided by count)

Probability Formula — Basic Probability Calculation

P(A) = Number of Favourable Outcomes ÷ Total Number of Possible Outcomes

Median Formula — How to Find the Middle Value

Odd n: Median = value at position (n+1)/2
Even n: Median = average of values at positions n/2 and n/2+1

Variance Formula — Statistics

Population Variance: σ² = Σ(xᵢ − μ)² ÷ N
Sample Variance: s² = Σ(xᵢ − x̄)² ÷ (n−1)

Mean, Median & Mode Formulas — Central Tendency Explained

Mean (x̄) = Σx / n
Median = middle value (or avg of 2 middle values)
Mode = most frequently occurring value

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Conversion Formulas

2

Celsius to Fahrenheit Formula — °C to °F Conversion

°F = (°C × 9/5) + 32 OR °F = (°C × 1.8) + 32

Kilograms to Pounds Formula — kg to lbs Conversion

lbs = kg × 2.20462

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Science Formulas

6

Molarity Formula — Chemistry

Ideal Gas Law Formula

Newton's Second Law Formula — Force = Mass × Acceleration

Velocity Formula — v = d/t and Acceleration Equations

Average Velocity: v = d / t
Final Velocity: v = u + at
Velocity²: v² = u² + 2as
Displacement: s = ut + ½at²

Density Formula — Mass ÷ Volume (ρ = m/V)

pH Formula — pH = -log[H⁺] Explained

pH = -log₁₀[H⁺]
pOH = -log₁₀[OH⁻]
pH + pOH = 14

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Engineering Formulas

5

Ohm's Law Formula — V = IR Explained

Force Formula — Newton's Second Law

Kinetic Energy Formula

KE = ½ × m × v²

Gravitational Potential Energy Formula

GPE = m × g × h

Pressure Formula — Physics

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business Formulas

7

Gross Profit Margin Formula — Business Profitability

Gross Margin = ((Revenue − COGS) ÷ Revenue) × 100

Markup Formula — Pricing Strategy Calculation

Markup % = ((Selling Price − Cost) ÷ Cost) × 100

Break-Even Formula — Fixed Costs ÷ Contribution Margin

Break-Even Units = Fixed Costs ÷ (Selling Price − Variable Cost Per Unit)
Break-Even Revenue = Fixed Costs ÷ Contribution Margin Ratio

Payback Period Formula

Payback Period (years) = Initial Investment ÷ Annual Net Cash Inflow

Gross Profit Formula — Revenue Minus Cost of Goods Sold

Gross Profit = Revenue − COGS
Gross Profit Margin (%) = (Gross Profit / Revenue) × 100

Customer Lifetime Value (LTV) Formula

LTV = ARPU × Average Customer Lifespan
LTV = ARPU / Churn Rate
LTV:CAC Ratio = LTV / CAC

Churn Rate Formula — How to Calculate Customer Churn

Monthly Churn Rate = (Customers Lost in Month / Customers at Start) × 100
Annual Churn Rate ≈ 1 − (1 − Monthly Churn)^12
Retention Rate = 100 − Churn Rate

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construction Formulas

2

Concrete Volume Formula — Cubic Yards and Meters

Volume (ft³) = Length (ft) × Width (ft) × Depth (ft)
Cubic Yards = Volume (ft³) ÷ 27
Cubic Meters = Length (m) × Width (m) × Depth (m)

Square Footage Formula — Length × Width

ft² = length (ft) × width (ft)

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social-media Formulas

1

Engagement Rate Formula — Social Media

ER = (Likes + Comments + Saves + Shares) / Followers × 100

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daily-life Formulas

4

Fuel Cost Formula — Trip Gas Cost

Cost = (Miles / MPG) × Price per Gallon

Electricity Cost Formula — kWh × Rate

Cost = (Watts × Hours ÷ 1000) × Rate

Age Formula — From Date of Birth

Age = Current Year − Birth Year − (birthday not yet passed ? 1 : 0)

Time Difference Formula — Hours Between Times

Diff = End − Start (add 24h if crossing midnight)

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