How to Calculate Percentages in Your Head and on Paper

Percentage simply means "per hundred". The universal formula is: (Part / Whole) × 100 = Percentage %.

Conversely, to find X% of Y: Multiply Y by X, then divide by 100.

To find 10% of any number, move the decimal point one place to the left ($64.00 becomes $6.40).

To find 1% of any number, move the decimal point two places to the left ($64.00 becomes $0.64).

To calculate a 15% tip on $60: 10% is $6. Half of that (5%) is $3. Sum them: $6 + $3 = $9 tip! This build-it-up approach scales to almost any percentage — need 35%? Take three 10% chunks plus one 5% chunk. Because you are only ever working with easy fractions of the number, you can do it reliably without a calculator.

A percentage increase measures how much a value has grown relative to where it started. The formula is: Increase % = ((New Value - Original Value) / Original Value) × 100. The key detail people miss is that you always divide by the ORIGINAL value, not the new one — the starting point is your reference.

For example, if a salary rises from $60,000 to $69,000, the increase is (69,000 - 60,000) / 60,000 × 100 = 15%. The same logic applies to a stock that climbs from $40 to $50 (a 25% gain) or website traffic that grows from 2,000 to 3,000 visits (a 50% increase).

A common source of confusion is that percentage increases can exceed 100%. If a value doubles, that is a 100% increase; if it triples, that is a 200% increase. Percentages describe change relative to the start, so there is no ceiling on how large an increase can be.

A percentage decrease works the same way but measures a drop. The formula is: Decrease % = ((Original Value - New Value) / Original Value) × 100. Again, you divide by the original value.

If a jacket is marked down from $120 to $90, the decrease is (120 - 90) / 120 × 100 = 25%, so it is "25% off". This is exactly the math behind every retail discount tag, and knowing it lets you verify a sale price in your head before you reach the register.

Unlike increases, decreases have a natural limit: for a value that cannot go below zero, the maximum possible decrease is 100% (the value drops to nothing). If you ever compute a decrease greater than 100%, it is a sign that an input was entered incorrectly.

It is tempting to assume that a 20% increase followed by a 20% decrease returns you to where you started. It does not. Suppose a price starts at $100 and rises 20% to $120. A subsequent 20% decrease is calculated on $120, not $100, so it falls by $24 to $96 — leaving you 4% below the original.

This asymmetry matters in finance, retail markdowns, and investing. Whenever a value changes and then changes back by the same percentage, the reference amount has shifted, so the two moves rarely cancel out. When in doubt, calculate each step against its own starting value rather than trusting your intuition.