How it's calculated
Every percentage problem is a variation on one idea: a percentage is a fraction out of 100. The three modes on this page cover the cases people actually meet — discounts, shares, raises and growth rates:
X is what % of Y = (X ÷ Y) × 100
% change = ((new − old) ÷ old) × 100
Watch the base. A 50% increase followed by a 50% decrease does not return you to the start: $100 → $150 → $75. The second 50% is taken from a bigger number. Always note which value the percentage is of.
Frequently asked questions
How do I calculate X percent of Y?
Convert the percentage to a decimal by dividing by 100, then multiply by Y. For example, 20% of 150 = 0.20 × 150 = 30. A shortcut: 10% of any number is the number with the decimal point moved one place left, so 20% is just double that.
How do I find the percentage increase between two numbers?
Subtract the old value from the new value, divide the difference by the old value, and multiply by 100. Formula: ((new − old) ÷ old) × 100. If the result is negative, it is a percentage decrease.
What is the difference between percent and percentage points?
Percentage points measure the absolute difference between two percentages; percent change measures the relative difference. If a rate rises from 10% to 15%, that is a 5 percentage-point increase but a 50% relative increase. Mixing them up is one of the most common statistics mistakes.
How do I reverse a percentage to find the original value?
If a value grew by p% to reach the final amount, the original = final ÷ (1 + p/100). If it shrank by p%, the original = final ÷ (1 − p/100). For example, a $230 price after a 15% increase came from 230 ÷ 1.15 = $200.
Disclaimer: results are arithmetic estimates for education and everyday use. For tax, payroll or contractual percentages, confirm with the relevant authority or a qualified professional.
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