%d terms, formulas and shortcuts
Percentage & finance cheat sheet
A single-page reference for the percentage math, statistics, finance and business metrics that come up in everyday work. Definitions, formulas, mental-math shortcuts and links to the on-site calculator for each topic.
Percentage basics
Open calculator- Percent / Percentage
- A number expressed as a fraction of 100. 25% means 25 out of 100, or 0.25 in decimal form.percent = (part / whole) × 100
- Percentage point
- The absolute difference between two percentages, not a percent change. A move from 5% to 7% is a 2 percentage-point increase — but a 40% relative increase.
- Basis point (bp)
- One one-hundredth of a percentage point. 50 basis points = 0.50%. Used to talk about interest rate changes precisely.1 bp = 0.01%
- Percent change
- The relative change between two values. Positive for increase, negative for decrease.((new − old) ÷ old) × 100
- Reverse percentage
- Finding the original number when you know the result and the percentage applied.original = result ÷ (percent ÷ 100)
- Stacked / compound discount
- Two or more discounts applied in sequence. They do not simply add — they multiply on the remaining percentages.final = original × (1 − r₁) × (1 − r₂)
- Per mille (‰)
- Per thousand, analogous to percent but on base 1000. 25‰ = 2.5%. Used in alcohol concentration and some tax rates.
Statistics
Open calculator- Mean
- The arithmetic average — sum of all values divided by the count.
- Median
- The middle value when data is sorted. Robust to outliers in a way the mean isn't.
- Mode
- The most frequently occurring value in a dataset.
- Percentile
- The value below which a given percentage of observations fall. The 90th percentile is the value below which 90% of data sits.
- Quartile
- Values that divide a sorted dataset into four equal parts: Q1 (25th percentile), Q2 (median), Q3 (75th percentile).
- IQR (Interquartile range)
- The middle 50% of the data: Q3 minus Q1. Used to spot outliers and measure spread.
- Standard deviation
- A measure of how spread out values are from the mean. Larger SD = more variability.
- Weighted average
- An average where each value has a different weight. Used in portfolio returns and grade calculations.Σ(weight × value) ÷ Σ(weight)
Finance & investment
Open calculator- Simple interest
- Interest calculated only on the original principal, not on accumulated interest.I = P × r × t
- Compound interest
- Interest calculated on the principal plus previously accumulated interest. Grows faster than simple interest over time.A = P(1 + r/n)^(nt)
- APR (Annual Percentage Rate)
- The yearly cost of a loan or credit, expressed as a percentage. Includes interest but not all fees.APR = ((interest + fees) ÷ principal) × (365 ÷ days) × 100
- APY / AER
- Annual percentage yield (US) / annual equivalent rate (UK). The true annual return after compounding is factored in.APY = (1 + r/n)^n − 1
- ROI (Return on Investment)
- The percentage gain or loss on an investment, relative to its cost.ROI = ((revenue − cost) ÷ cost) × 100
- IRR (Internal Rate of Return)
- The discount rate at which the net present value of cash flows is zero. Used to compare investments with different timing.
- CAGR
- Compound Annual Growth Rate — the smoothed annualized growth rate over a multi-year period.CAGR = (end/start)^(1/years) − 1
- NPV (Net Present Value)
- The current value of future cash flows, discounted at a chosen rate. Positive NPV means the investment is worth pursuing.
- EMI
- Equated Monthly Installment — fixed monthly payment on a loan that combines principal and interest.
- Amortization
- The process of paying off a loan in regular installments where each payment covers a shrinking portion of interest and growing portion of principal.
- Principal
- The original amount of money borrowed or invested, before any interest accrues.
- Yield
- The income return on an investment, typically expressed as a percentage of cost or current price.
- Inflation
- The percentage rate at which a basket of goods rises in price over time. Erodes the purchasing power of money.
- Real vs nominal
- Nominal is the headline number; real is the number adjusted for inflation. Real return is what your money actually bought you.
Business metrics
Open calculator- Profit margin
- Profit as a percentage of revenue. Higher is better.margin = ((revenue − cost) ÷ revenue) × 100
- Markup
- The amount added to cost to set the selling price, expressed as a percentage of cost (not revenue). Often confused with margin.markup = ((price − cost) ÷ cost) × 100
- Gross margin
- Revenue minus the direct cost of goods sold, expressed as a percentage of revenue.gross margin = ((revenue − COGS) ÷ revenue) × 100
- Net margin
- The bottom-line margin after all expenses, taxes and interest are subtracted.
- Conversion rate
- The percentage of visitors who complete a desired action (purchase, signup, click).conversion = (conversions ÷ total visitors) × 100
- Churn rate
- The percentage of customers who cancel or stop using a service over a given period.
- Customer lifetime value (LTV)
- The total revenue a typical customer generates over their relationship with the business.
- CAC (Customer Acquisition Cost)
- The total cost of marketing and sales divided by the number of new customers acquired in the same period.
- Market share
- A company's sales as a percentage of total industry sales.market share = (own sales ÷ total market sales) × 100
Tax & consumer math
Open calculator- VAT (Value Added Tax)
- A consumption tax applied to goods and services at each stage of the supply chain. Used across the EU, UK and most of the world outside the US.
- Sales tax
- A consumption tax applied at the point of final sale only. Used in the US (varies by state) and a few other countries.
- GST (Goods and Services Tax)
- A national consumption tax used in countries like India, Canada, Australia, Singapore and New Zealand. Mechanism similar to VAT.
- Net price
- The price before tax is added. What the seller actually receives.
- Gross price
- The price including tax. What the buyer pays at the till.
- Tip percentage
- A gratuity expressed as a percentage of the pre-tax bill. Typical US tip is 18–20% on the pre-tax total.
- Discount percentage
- A reduction in the original price expressed as a percent. The "you save" line.discount $ = original × (percent ÷ 100)
- Dynamic currency conversion (DCC)
- The "pay in your home currency or local" prompt at a foreign card terminal. Always pick local currency — DCC adds a 4–8% markup.
Mental-math shortcuts
Open calculator- 10% shortcut
- Move the decimal point one place to the left. 10% of 347 = 34.7.
- 5% shortcut
- Half of 10%. 5% of 347 = 17.35.
- 15% shortcut
- 10% + 5%. 15% of 347 = 34.7 + 17.35 = 52.05.
- 20% shortcut
- Double 10%. 20% of 347 = 69.4.
- 25% shortcut
- Divide by 4. 25% of 347 = 86.75.
- 50% shortcut
- Divide by 2.
- 75% shortcut
- Three-quarters: original × 3 ÷ 4.
- X% of Y = Y% of X
- A surprising identity. 4% of 75 is the same as 75% of 4 — both equal 3. Sometimes the reversed form is easier to compute.
- Rule of 72
- Estimate how many years it takes money to double at a given annual return: divide 72 by the percentage rate. At 7%, money doubles in about 10.3 years.
- Rule of 70
- Variant of Rule of 72 — sometimes a closer approximation at lower rates. Same idea: divide 70 by the rate to get doubling time.