How to Calculate Percentage Increase (and Decrease) Step by Step

Percentage increase and decrease use the same underlying formula, and the single most common mistake — dividing by the wrong number — is worth understanding clearly once, since it’s an easy error to make under time pressure and a genuinely confusing one to spot afterward.

The formula

Percentage change is calculated as: ((New Value − Old Value) / Old Value) × 100. The key detail, and the source of most errors, is that you always divide by the original value, not the new one — the percentage change is always relative to where you started, not where you ended up.

A value going from 50 to 65 increased by 15 in absolute terms. Divide that 15 by the original 50, not the new 65: 15 ÷ 50 = 0.30, or a 30% increase. A value going from 200 down to 150 decreased by 50; divide by the original 200: −50 ÷ 200 = −0.25, a 25% decrease. The negative sign in the second example is exactly why the same formula handles both increase and decrease — a positive result means growth, a negative result means decline, with no need for a separate “decrease” formula.

Why dividing by the wrong number breaks everything

Swapping to divide by the new value instead of the old one seems like a minor slip but produces a genuinely different — and wrong — answer. Take the 50-to-65 example again: dividing the 15-point gain by 65 (the new value) instead of 50 (the original) gives about 23.1%, not the correct 30%. Both numbers look plausible in isolation, which is exactly what makes this mistake hard to self-catch — the error doesn’t produce an obviously broken result, just a subtly wrong one.

A reliable way to keep the direction straight: “percentage change relative to what” always means relative to the starting point, the value things were compared against, never the ending point.

A genuinely common real-world trap: reversing a percentage change

Here’s a scenario that trips up a lot of people specifically because the intuitive answer feels right but isn’t: if a price increases by 20%, does decreasing the new price by 20% bring you back to the original price? No — and the reason is exactly the “divide by the original value” rule above, applied twice on two different base values.

A $100 item increased by 20% becomes $120. Decreasing $120 by 20% means subtracting 20% of $120 (which is $24), not 20% of the original $100 — landing at $96, not back at $100. The percentage is the same (20%) both times, but it’s applied to two different base amounts, which is exactly why a percentage increase and an equal-sized percentage decrease never fully cancel out except in the special case of a 0% change. This asymmetry is genuinely important in real financial contexts — a stock that drops 50% needs a 100% gain (not 50%) to fully recover, precisely because the recovery percentage is calculated against the new, smaller base.

Percentage change vs percentage points

Phrasing	From 20% to 25%
Percentage points	5 point increase (25 − 20)
Percentage change	25% increase (5 ÷ 20 × 100)

One more distinction worth being precise about: a change from 20% to 25% is correctly described as either “a 5 percentage point increase” or “a 25% increase” — and these two phrasings describe genuinely different things, not two ways of saying the same thing. The percentage-point figure (5) is the simple arithmetic difference between the two percentages; the percentage-change figure (25%) is that same 5-point gap expressed relative to the original 20% baseline, using the standard percentage-change formula above. Financial and statistical reporting is often sloppy about this distinction in ways that can genuinely mislead — always check whether a reported “percentage increase” in a rate or ratio actually means percentage points or true percentage change, since conflating the two can make a modest change sound dramatically larger (or a large change sound smaller) than it really is.

Calculating it directly

The Percentage Change Calculator on this site applies the correct original-value-denominator formula directly — enter your old and new values and it handles the sign and division correctly every time, removing the risk of the divide-by-the-wrong-number mistake entirely. For basic “what is X% of Y” or “X is what percent of Y” questions rather than a before/after comparison, the Percentage Calculator covers those directly-related but distinct calculations, and the Percentage Error Calculator applies the same core formula to compare a measured or estimated value against a known true value.