Math and Money Glossary: Plain Definitions With a Calculator for Each

Short answer: this page defines the terms that cause the most confusion in everyday calculations, one precise sentence each, and links every term to the matching Mathify calculator. Where two terms are often swapped, such as markup and margin, the entry says how they differ. Finance and health entries are general definitions, not advice.

Percentages and ratios

Percentage. A number expressed as a part of 100, so 25% means 25 out of every 100. Calculator: Percentage Calculator.

Percentage point. The plain difference between two percentages, so a move from 40% to 46% is 6 percentage points. Calculator: Percentage Calculator.

Percent change. The difference between a new and an old value divided by the old value, expressed as a percentage. Calculator: Percentage Calculator.

Basis point. One hundredth of a percentage point, so 100 basis points equal 1 percentage point. Calculator: Basis Point Calculator.

Ratio. A comparison of two quantities, written as a:b, that tells you how many times one contains the other. Calculator: Ratio Calculator.

Fraction. A number written as one integer over another, which represents division. Calculator: Fraction Calculator.

Statistics

Mean. The sum of the values divided by how many there are. Calculator: Mean, Median and Mode Calculator.

Median. The middle value of a sorted list, or the average of the two middle values when the count is even. Calculator: Mean, Median and Mode Calculator.

Mode. The value that appears most often, if any value repeats. Calculator: Mean, Median and Mode Calculator.

Standard deviation. A measure of how far values typically sit from their mean, calculated as the square root of the variance. Calculator: Standard Deviation Calculator.

Probability. A number from 0 to 1 (or 0% to 100%) that measures how likely an event is. Calculator: Probability Calculator.

Interest and growth

Principal. The original amount borrowed or invested, before any interest is added. Calculator: Simple Interest Calculator.

Simple interest. Interest calculated only on the principal, equal to principal times rate times time. Calculator: Simple Interest Calculator.

Compound interest. Interest calculated on the principal plus the interest already added in earlier periods. Calculator: Compound Interest Calculator.

APR (annual percentage rate). The yearly rate quoted for a loan or account before the effect of compounding within the year. Calculator: APR Calculator.

APY (annual percentage yield). The yearly rate after compounding is counted, so it is higher than the APR when interest compounds more than once a year. Calculator: APY Calculator.

CAGR (compound annual growth rate). The constant yearly growth rate that would take a starting value to an ending value over a given number of years. Calculator: CAGR Calculator.

Rule of 72. A shortcut that estimates the years to double by dividing 72 by the annual percentage rate. Calculator: Rule of 72 Calculator.

Inflation. A general rise in prices over time, which reduces what a unit of money buys. Calculator: Inflation Calculator.

Real return. An investment return after the effect of inflation has been removed. Calculator: Real Return Calculator.

Loans and valuation

Amortization. Paying off a loan through scheduled payments that each cover interest first and reduce the balance with the remainder. Calculator: Loan Calculator.

EMI (equated monthly instalment). A fixed monthly payment that repays both principal and interest over the loan term. Calculator: EMI Calculator.

Debt-to-income ratio. Monthly debt payments divided by gross monthly income, shown as a percentage. Calculator: Debt-to-Income Calculator.

Present value. What a future sum of money is worth today when discounted at a chosen rate. Calculator: Present Value Calculator.

Net present value (NPV). The sum of the present values of all future cash flows minus the starting cost. Calculator: Net Present Value Calculator.

IRR (internal rate of return). The discount rate at which the net present value of a series of cash flows equals zero. Calculator: IRR Calculator.

Net worth. Total assets minus total liabilities. Calculator: Net Worth Calculator.

Business and pricing

Markup. The profit as a percentage of the cost, calculated as (price minus cost) divided by cost. Calculator: Markup Calculator.

Margin. The profit as a percentage of the selling price, calculated as (price minus cost) divided by price. A cost of 80 sold at 100 is a 25% markup and a 20% margin. Calculator: Margin Calculator.

Break-even point. The sales volume at which total revenue equals total cost, so profit is zero. Calculator: Break-Even Calculator.

ROI (return on investment). The gain from an investment divided by its cost, shown as a percentage. Calculator: ROI Calculator.

Discount. A reduction from the original price, usually shown as a percentage off. Calculator: Discount Calculator.

Sales tax. A percentage added to the price of goods at the point of sale. Calculator: Sales Tax Calculator.

Health

BMI (body mass index). Weight in kilograms divided by height in metres squared, used as a rough screening number. Calculator: BMI Calculator.

BMR (basal metabolic rate). An estimate of the energy the body uses at complete rest over a day. Calculator: BMR Calculator.

Dates and time

Leap year. A year with 366 days, which in the Gregorian calendar is any year divisible by 4, except century years not divisible by 400. We checked that 2000 and 2024 are leap years and 1900, 2026 and 2100 are not. Calculator: Days in Month Calculator.

Business day. A weekday that is not a public holiday, and the unit used for many deadlines. Which days count depends on the country and employer. Calculator: Business Days Calculator.

Unix timestamp. The number of seconds since 1 January 1970 at 00:00:00 UTC. Calculator: Unix Timestamp Converter.

Time zone offset. The difference between local time and UTC, which changes in places that observe daylight saving. Calculator: Time Zone Converter.

Related reading

For the mistakes behind some of these terms, see percent vs percentage points, simple vs compound interest and APR vs APY and mean vs median vs mode.

Definitions here are general and simplified. Rules for terms like APR, business days and tax differ by country and product, so rely on the source document for any decision. Health and finance entries are for information, not advice.

FAQ

What is the difference between APR and APY?

APR is the quoted yearly rate before compounding within the year. APY includes the effect of compounding, so for a 5% APR compounded monthly, the APY is 5.1162%.

What is the difference between markup and margin?

Markup divides profit by cost, margin divides profit by selling price. For a cost of 80 and a price of 100, markup is 25% and margin is 20%.

What is a percentage point?

It is the plain difference between two percentages. A rate that rises from 4% to 5% has risen 1 percentage point.

Is the median the same as the average?

Not necessarily. The average usually means the mean. The median is the middle value of a sorted list, and the two differ when the data is skewed.

Can an AI assistant use these calculators for me?

Yes, if your assistant supports custom connectors. The guide to connecting Mathify calculators to an AI assistant explains the steps.