How to Calculate Percentage Increase Between Two Numbers

A salary rises from $4,200 a month to $4,830 a month. A product price moves from $48 to $60. A website’s monthly visitors grow from 12,000 to 15,600. In each case, the raw change is easy to state — $630 more, $12 more, 3,600 more visitors — but the raw change alone does not say how large the move is relative to where it started. That is what percentage increase is for: it expresses a change as a share of the starting value, so a $630 rise on a $4,200 salary and a $630 rise on a $63,000 salary are not confused with each other.

This guide gives the exact formula, works one complete example step by step, and then covers the cases where percentage increase most often goes wrong: decreases that look like increases, increases and decreases that do not cancel out, successive percentage changes that do not add up, and the difference between percentage points and percent.

The formula

Percentage increase = (New value − Old value) ÷ Old value × 100

The three steps, in order, are:

1. Find the difference: subtract the old value from the new value.
2. Divide by the old value: this is the step that matters most, because the old value — the starting point — is always the denominator.
3. Multiply by 100: this converts the decimal result into a percentage.

A positive result means an increase. A negative result means a decrease, and it is usually reported as a percentage decrease instead — for example, a result of −20% is a 20% decrease. A result of zero means no change. The formula works for money, prices, counts, scores, and any other quantity measured on a scale where zero means none of that quantity, provided the old value is not zero. When the old value is zero, percentage increase is undefined, because division by zero has no answer — a point returned to below.

Worked example: a salary from $4,200 to $4,830 a month

Take a monthly salary that rises from $4,200 to $4,830. The old value is $4,200, because that is where the salary started. The new value is $4,830.

Step 1 — Difference. $4,830 − $4,200 = $630. The salary is $630 a month higher than before.

Step 2 — Divide by the old value. $630 ÷ $4,200 = 0.15. In other words, the rise is fifteen hundredths of the starting salary.

Step 3 — Multiply by 100. 0.15 × 100 = 15%.

So the salary increased by 15%. Two checks confirm the answer. First, 15% of the old salary is 0.15 × $4,200 = $630, which is exactly the difference found in step 1. Second, the new salary can be rebuilt from the old salary and the percentage: $4,200 × 1.15 = $4,830. The multiplier 1.15 is simply 1 plus the percentage as a decimal (1 + 0.15), and it is a useful shortcut: to increase any number by a percentage, multiply it by 1 plus that percentage divided by 100. The annual raise calculator applies the same logic to a yearly salary, so a hand calculation should match it to within rounding.

The annual figures tell the same story. Over a year, the old salary is $4,200 × 12 = $50,400 and the new salary is $4,830 × 12 = $57,960. The difference is $7,560, and $7,560 ÷ $50,400 × 100 = 15% again. Scaling both values by the same factor — here, by 12 months — leaves the percentage unchanged, which is why a monthly increase and the equivalent annual increase are the same percentage.

A second check: a price from $48 to $60

The same three steps work on a smaller scale. A product priced at $48 rises to $60.

Difference: $60 − $48 = $12. Divide by the old value: $12 ÷ $48 = 0.25. Multiply by 100: 25% increase.

The check works the same way: 25% of $48 is $12, and $48 × 1.25 = $60. Notice that a $12 rise is 25% here but would be a very different percentage on a different base: $12 on a $120 starting price is only 10%, and $12 on a $24 starting price is 50%. The percentage always depends on the starting value, never on the size of the change alone. That is why reporting “prices rose by $12” and reporting “prices rose by 25%” answer different questions, and why a news headline that gives only one of them is incomplete.

The most common mistake: dividing by the new value

The single most common error in percentage increase is using the new value as the denominator instead of the old value. On the salary example, that error gives $630 ÷ $4,830 × 100 = 13.04%, not 15%. On the price example, it gives $12 ÷ $60 × 100 = 20%, not 25%. Both wrong answers are smaller than the correct ones, which makes the error easy to miss: the result still looks plausible.

The reason the old value is the denominator is definitional. A percentage increase answers the question “by what fraction of where I started did I grow?” The starting point is the reference, so it goes underneath the division. Dividing by the new value answers a different question — what share of the final value the change represents — and that is not a percentage increase. Whenever a calculated increase looks suspiciously small, the first thing to check is which value was used as the denominator.

A related error is dividing by the difference itself, or forgetting the × 100 step and reporting 0.15 instead of 15%. The decimal 0.15 and the percentage 15% are the same quantity written two ways, but in a report, a contract, or a salary letter, the wrong form changes the meaning: a “0.15 increase” will be read as 0.15%, not 15%.

Why a rise and a fall of the same size do not cancel out

Percentage changes are not symmetric, because each change is measured against a different base. The price example shows this clearly. The price rises from $48 to $60, a 25% increase. If it then falls back from $60 to $48, the fall is $12 ÷ $60 × 100 = 20% decrease — not 25%. The dollar move is the same $12 in both directions, but the percentage differs because the second move is measured against $60, a larger base.

The same asymmetry explains a familiar investing puzzle. An investment that falls by 20%, from $100 to $80, needs a rise of $20 ÷ $80 × 100 = 25% just to get back to $100 — not 20%. A fall of 50%, from $100 to $50, needs a 100% rise to recover, because the $50 that must be regained is the whole of what remains. In general, recovering from a fall of p percent requires a rise of p ÷ (100 − p) × 100 percent: after a 10% fall, a rise of 11.11% is needed; after a 25% fall, a rise of 33.33% is needed; after a 50% fall, a rise of 100% is needed. Anyone comparing a gain and a loss should therefore never assume they offset each other unless the bases are the same.

This asymmetry also matters when a figure is quoted without its base. A claim that “sales rose 25% and then fell 25%” does not return sales to their starting point: $100 rising 25% becomes $125, and $125 falling 25% becomes $93.75, which is 6.25% below where it started. The two percentages look equal, but they apply to different amounts.

Successive increases do not add up

Two successive percentage increases cannot simply be added together, because the second increase applies to the already-increased value, not to the original. A price that rises by 10% and then by 10% again has not risen by 20%.

Start at $100. A 10% rise gives $100 × 1.10 = $110. A second 10% rise gives $110 × 1.10 = $121. The total increase is $21 on a $100 base, or 21%, not 20%. With three successive 5% rises, the multiplier is 1.05 × 1.05 × 1.05 = 1.157625, a total increase of 15.76%, not 15%. The gap grows with the size of the percentages: two successive 50% rises give 1.50 × 1.50 = 2.25, a 125% total increase, not 100%.

The rule is to multiply the multipliers, not to add the percentages. To combine increases of a% and b%, the total increase is ((1 + a ÷ 100) × (1 + b ÷ 100) − 1) × 100. The same rule works when one change is a decrease: a 20% rise followed by a 10% fall gives 1.20 × 0.90 = 1.08, an overall increase of 8%, not 10%. The investment calculator and compound interest calculator apply this compounding logic over many periods, which is why a steady annual growth rate produces a much larger total gain over a decade than the annual rate multiplied by ten would suggest.

A practical consequence is that stacked discounts work the same way. A 30% discount followed by a further 10% discount is not a 40% discount: the second discount applies to the price after the first, so the combined multiplier is 0.70 × 0.90 = 0.63, a total saving of 37%. The discount off calculator shows this combined effect directly, and it is worth checking whenever a retailer advertises stacked percentage offers.

Percentage points are not the same as percent

When the quantity being measured is itself a percentage, a change in that quantity can be described two ways, and confusing them is a frequent source of misleading headlines. If an interest rate rises from 4% to 5%, the change is 1 percentage point — the simple arithmetic difference between the two rates. The percentage increase in the rate, however, is (5 − 4) ÷ 4 × 100 = 25%. Both statements are true, and they mean different things: the rate is one point higher, and it is a quarter larger than it was.

The distinction matters most for rates, tax rates, market shares, and exam pass rates. A pass rate rising from 60% to 66% is a 6-percentage-point improvement and a 10% relative increase (6 ÷ 60 × 100). A report that says only “pass rates rose 10%” is correct in relative terms but understates the absolute improvement for a reader who assumes percentage points; a report that says only “pass rates rose 6%” without specifying points is ambiguous. The safe practice is to state both when the base is itself a percentage, or to write “percentage points” in full when that is what is meant.

Working backwards: finding the original value

Sometimes the new value and the percentage increase are known, but the original value is not. The formula reverses cleanly: divide the new value by the multiplier.

Suppose a price after a 15% increase is $138. The multiplier is 1.15, so the original price was $138 ÷ 1.15 = $120. The check is $120 × 1.15 = $138. Similarly, a salary that is $4,830 after a 15% raise had a pre-raise value of $4,830 ÷ 1.15 = $4,200, which returns to the main example.

The common error here is to subtract the percentage from the new value instead: 15% of $138 is $20.70, and $138 − $20.70 = $117.30, which is wrong. The 15% was calculated on the original $120, not on the final $138, so subtracting 15% of the final value removes too much. The same warning applies to sale prices: a price of $90 after a 10% discount was not $99 (90 + 10% of 90), but $100, because $90 ÷ 0.90 = $100. Reversing a percentage always means dividing by the multiplier, never adding or subtracting a percentage of the final figure. The percent markup calculator is built around this reverse direction for cost and selling price.

When the old value is zero, negative, or very small

Three edge cases deserve care. First, when the old value is zero, percentage increase is undefined: a business that goes from 0 customers to 50 customers has grown by 50 customers, but there is no meaningful percentage, because 50 ÷ 0 has no answer. Reporting “infinite growth” or an invented percentage in that case is misleading; the absolute change is the honest figure.

Second, when values can be negative — profits turning into losses, or temperatures below zero — the standard formula can produce nonsense. A profit moving from −$100 to −$50 is an improvement of $50, but (−50 − (−100)) ÷ (−100) × 100 = −50%, which reads as a decrease. In such cases, percentage change should either be avoided in favour of the absolute change, or calculated against the absolute value of the base with the direction stated in words.

Third, when the old value is very small, a modest absolute change produces a huge percentage that exaggerates the story. Visitors rising from 4 a day to 20 a day is a 400% increase, which is arithmetically correct and practically unimpressive. With small bases, always give the absolute numbers alongside the percentage so the reader can judge the scale.

Adjusting for inflation: nominal increase vs real increase

A salary increase is only a genuine improvement if it outpaces rising prices. If a salary rises by 15% while prices rise by 6%, the real increase — the increase in what the salary can buy — is not 15% − 6% = 9%. The correct calculation divides the multipliers: 1.15 ÷ 1.06 = 1.0849, a real increase of about 8.49%. The subtraction shortcut is close when both percentages are small, but it drifts as they grow: a 50% salary rise against 20% inflation is a real increase of 1.50 ÷ 1.20 − 1 = 25%, not 30%.

On the main example, a $4,200 salary rising 15% to $4,830 buys about 8.49% more than before if prices rose 6% over the same period. The inflation calculator and interest calculator are useful companions here: one adjusts a sum for price changes, the other separates the nominal return on a sum from its growth in real terms. A pay rise that merely matches inflation is a 0% real increase, however large the nominal percentage looks.

A table of worked examples

Each row uses the same three steps, and each check rebuilds the new value from the old value and the percentage: old × (1 + percentage ÷ 100) = new. If that check fails, one of the inputs or the denominator is wrong.

How to do it in a spreadsheet

In a spreadsheet, with the old value in cell A1 and the new value in B1, the formula is =(B1-A1)/A1 formatted as a percentage, or =(B1-A1)/A1*100 for a plain number. The same cell-reference discipline applies as on paper: the denominator must be the old value’s cell. A common spreadsheet error is to copy the formula down a column after inserting a new row, so the denominator silently points at the new value instead of the old one; checking one row by hand against the three steps above catches that immediately. For a column of successive values, each row’s increase should be calculated against the previous row, not against the first row — unless the question being asked is the total increase from the start, in which case the first row is the correct denominator for every row.

Frequently asked questions

What is the formula for percentage increase?

Percentage increase = (New value − Old value) ÷ Old value × 100. Subtract the old value from the new value, divide the difference by the old value, and multiply by 100. For example, $4,200 to $4,830 is ($4,830 − $4,200) ÷ $4,200 × 100 = 15%.

How is percentage increase different from percentage difference?

Percentage increase is directional: it measures a move from a starting value to a later value, using the starting value as the base. Percentage difference is symmetric: it measures the gap between two values using their average as the base, so it gives the same answer whichever value is listed first. From $48 to $60, the percentage increase is 25%, but the percentage difference is $12 ÷ (($48 + $60) ÷ 2) × 100 = 22.22%. Use percentage increase when there is a before and an after; use percentage difference when comparing two measurements with no direction, such as two survey results.

Can percentage increase be more than 100%?

Yes. A percentage increase above 100% simply means the new value is more than double the old value. A rise from $50 to $150 is ($150 − $50) ÷ $50 × 100 = 200%, because the $100 gain is twice the starting value. A 100% increase exactly doubles a value; a 200% increase triples it. There is no upper limit, though very large percentages on small bases should always be accompanied by the absolute numbers.

What if the new value is smaller than the old value?

Then the formula gives a negative result, which is reported as a percentage decrease. From $60 to $48, the result is −20%, stated as a 20% decrease. The arithmetic is identical; only the direction word changes. Do not force the result positive by swapping the values, because that changes the base and therefore the percentage.

Why do I get a different answer from an online calculator?

Almost always, one of three things differs: the denominator (new value used instead of old), the direction (the two values swapped), or rounding at an intermediate step. Rounding the decimal before multiplying by 100 is a quiet source of error: $630 ÷ $4,200 is exactly 0.15, but a messier division such as 7 ÷ 30 = 0.2333… rounded to 0.23 gives 23% instead of 23.33%. Keep full precision until the final step, then round the percentage — usually to one or two decimal places — at the end.

How do I calculate percentage increase when the numbers are not money?

Exactly the same way. Visitors from 12,000 to 15,600: (15,600 − 12,000) ÷ 12,000 × 100 = 30%. Test scores from 72 to 90: (90 − 72) ÷ 72 × 100 = 25%. The units cancel in the division, so the formula works for counts, weights, distances, scores, and any other quantity where zero means none of it. It does not work as a simple ratio for temperatures in Celsius or Fahrenheit, where zero is an arbitrary point on the scale rather than an absence of heat; for those, convert to an absolute scale first or report the absolute change.

Is a 15% salary increase good?

That depends on inflation, on what comparable roles pay, and on whether hours or responsibilities changed at the same time. In nominal terms, 15% is a substantial rise. In real terms, after 6% inflation, it is about 8.49% more purchasing power, as calculated above. If the increase came with longer hours, the hourly rate may have risen by less or not at all: a salary from $4,200 for 160 hours a month is $26.25 an hour, while $4,830 for 180 hours a month is $26.83 an hour, only a 2.2% hourly increase. Always check what else changed alongside the headline percentage before judging it.

Bottom line

Percentage increase = (New value − Old value) ÷ Old value × 100, with the old value always as the denominator. On the worked example, $4,200 to $4,830 is a $630 difference, $630 ÷ $4,200 = 0.15, and 0.15 × 100 = 15%. Remember the three traps: dividing by the new value understates the answer, equal-looking rises and falls do not cancel because their bases differ, and successive percentages multiply rather than add. Get the base right, keep full precision until the end, and check the answer by rebuilding the new value — old × (1 + percentage ÷ 100) — and the percentage will hold up wherever it is quoted.