How to calculate percentage increase (and decrease), step by step

Calculating percentage increase sounds like one skill, but in my experience it is the point where percentage math most often goes quietly wrong — not because the formula is hard, but because people divide by the wrong number. Calculating percentages of any kind always comes down to one discipline: know your starting value, because that is what you divide by. In this article I work three examples all the way through — a price, a salary and a headcount — then show decreases, then show the trap that catches almost everyone: a rise and a fall of the same percentage do not cancel out. Master this one formula and you have also answered the broader question of how to calculate a percentage in most real situations, because change is the form percentages take out in the wild.

How to calculate percent increase, in three steps

Every increase (and every decrease) follows the same three steps. When I am calculating percentage change of any kind, these are the steps I actually take:

1. Find the change. Subtract the old value from the new value. New minus old — the sign of the answer already tells you whether it is an increase or a decrease.
2. Divide by the old value. Not the new one, not the average — the value you started from. This step is where most errors creep in.
3. Multiply by 100 and attach the % sign. If step 1 gave you a negative number, you have a decrease; report its size as a positive percentage and say “decrease”.

The compressed version: percentage increase = ((new − old) ÷ old) × 100. Our percentage calculator runs exactly this formula in its percent change mode — the steps below are what it is doing under the hood.

Example 1: a price increase, $80 to $100

A jacket that cost $80 last season is $100 now. Step 1: the change is 100 − 80 = $20. Step 2: divide by the old price, 20 ÷ 80 = 0.25. Step 3: 0.25 × 100 = 25% increase. Note where the 0.25 came from — twenty dollars is a quarter of the old $80 price. If you had mistakenly divided by the new price, you would have got 20 ÷ 100 = 20%, a plausible-looking answer that is simply wrong, because the increase happened to the $80, not to the $100.

Example 2: a salary increase, $52,000 to $54,600

Salaries hide the arithmetic because the numbers are big, so let me shrink them honestly — the steps do not care about the zeros. The raise is 54,600 − 52,000 = $2,600. Divide by the old salary: 2,600 ÷ 52,000 = 0.05. Multiply by 100: a 5% increase. That is the number worth knowing, because a $2,600 raise on a $52,000 salary (5%) and a $2,600 raise on a $130,000 salary (2%) are very different negotiations wearing the same dollar amount.

Example 3: a count increase, 12,400 to 13,640

The formula is not only for money. A town whose population grows from 12,400 to 13,640 has added 1,240 people. Calculating percentage growth: 1,240 ÷ 12,400 = 0.10, so the town grew by 10%. Counts, measurements, traffic, subscribers — anything with an old value and a new value uses the identical three steps.

All four rows computed with the same formula: (new − old) ÷ old × 100. The only thing that changes between problems is what the numbers describe.

Four more, rapid-fire

The three worked examples above are the teaching set; here is the same formula running on the kinds of numbers that actually show up in a week. A rent rise from $1,200 to $1,350 a month: the change is $150, divided by the old rent of $1,200, so 12.5% — a number worth having before you sign anything. A grocery staple that went from $4.80 to $5.40 rose by 60 cents on a $4.80 base, also 12.5%, which is why small prices can hide large percentage rises. A working week lengthening from 37.5 to 40 hours is a rise of 2.5 hours on 37.5, or 6.67%. And a website growing from 8,200 to 12,300 visitors added 4,100 on a base of 8,200 — exactly 50%. Four unrelated problems, one formula, no new ideas needed.

Each row computed as (new − old) ÷ old × 100. Small bases produce large percentages from small absolute changes — the $0.60 grocery rise matches the $150 rent rise exactly.

Calculating a percentage decrease

A decrease is not a different formula — it is the same formula with a negative answer. A heater drops from $120 to $90: the change is 90 − 120 = −$30, divided by the old price of $120 gives −0.25, so the price fell by 25%. When you are calculating a percentage to report to someone, state the direction in words (“a 25% decrease”) and give the size as a positive number; the minus sign has already done its job by telling you which direction things moved.

The asymmetry: equal percentages do not cancel

Here is the trap. The jacket rose 25%, from $80 to $100. If it now falls 25%, does it return to $80? It does not. A 25% fall from $100 removes $25 and lands at $75 — because the fall is calculated on the new, larger base. To undo a 25% increase you need a fall of only 20%: 20% of $100 is $20, which takes you exactly back to $80. The rule runs both ways: a 25% decrease (say $100 down to $75) needs a 33.33% increase to undo it, because the climb back is measured from the smaller $75 base. Whenever calculating percentages across two steps, remember that each step gets a new base — percentages chain by multiplying, never by adding or cancelling.

Two increases in a row: growth on growth

One more shape worth seeing before you go, because it appears in every pay review and every rent letter: consecutive increases do not add either. A salary of $50,000 rises 5% to $52,500, then rises another 5% the following year. The second raise is 5% of $52,500 — $2,625, not $2,500 — so the salary lands at $55,125. Across the two years the total increase is $5,125 on a $50,000 start: 10.25%, not the 10% that adding the two percentages suggests. Each increase re-bases the next one, exactly as the asymmetry section warned. Calculating percentage growth over several periods always works this way: apply each step to the running total, never add the percentages and apply them once.

Three years of small increases: the inflation pattern

The chaining effect is not a curiosity — it is how prices actually move. Take a $100 item rising 4% a year, a modest inflation-style rate. After year one it costs $104. After year two, $108.16 — note the second rise was $4.16, not $4, because 4% now applies to $104. After year three, $112.49. Across the three years the total rise is 12.49%, not the 12% that three fours suggest. Half a percentage point sounds like nothing until it is applied to rent, tuition or a grocery bill for a decade, at which point the compounding gap is the difference between a budget that tracks reality and one that quietly falls behind it.

Each year computed as previous price × 1.04. The yearly rise grows in dollars even though the rate never changes — that growth in the increment is the signature of compounding.

Working backwards: finding the value before the increase

Sometimes you are handed the finished number and the percentage, and the question runs in reverse: what did this cost before the rise? The trap is to subtract the percentage from the new value — that repeats the wrong-base error in a new costume. The correct move is to divide by the multiplier. If a price after a 20% increase is $96, the original was 96 ÷ 1.20 = $80 — the same jacket from Example 1, recovered exactly. If a total of $54 already includes an 8% tax, the pre-tax price was 54 ÷ 1.08 = $50. And a salary reported as $125,000 after a 25% rise started at 125 ÷ 1.25 = $100,000. In each case, subtracting the percentage from the new number (96 − 20% of 96 = $76.80, for example) gives a wrong answer that looks perfectly reasonable, which is what makes this the most expensive mistake in this article.

The three mistakes I see most

• Dividing by the new value. The increase happened to the old value, so the old value is the base. 20 ÷ 100 instead of 20 ÷ 80 turns a 25% rise into a phantom 20%.
• Adding step percentages. Two consecutive 5% raises total 10.25%, not 10%, because the second raise is calculated on the already-raised amount.
• Reporting the change instead of the percentage. “Prices rose by $150” and “prices rose by 12.5%” are both true of the rent example, but only the second one lets anyone judge whether the rise is large — $150 on $1,200 and $150 on $400 (37.5%) are very different stories.

Sources: all figures computed for this article with the standard percent change formula, (new − old) ÷ old × 100. Dollar amounts are illustrative examples, not market data.