How this instrument works
Percentage increase measures how much larger a value has become, expressed as a percent of the value it started from. It is deliberately one-directional: the new figure is expected to be the bigger of the pair, and the result is always zero or positive. That restriction is not an oversight — plenty of real growth questions never ask 'which way did this move?' A raise, a price hike, or a year's growth in a population count already carry an assumed direction, so checking the sign and reporting a signed answer, the way the general percentage-change instrument does, is an extra step this page is built to skip.
The formula is (new − old) ⁄ old × 100, and each part earns its place. The numerator, new minus old, is the raw amount gained, in whatever unit the two figures share. Dividing by old rescales that raw gain against the size it grew from, which is exactly why an identical $25 raise reads as a dramatic 50% jump on a $50 wage but a barely-there 5% bump on a $500 one. Multiplying by 100 simply converts the resulting fraction into the percent notation people expect to read.
One consequence trips up almost everyone the first time: percentage increases do not add across repeated steps. A wage raised by 10% twice does not finish 20% above where it began — the second 10% is taken from the already-larger figure, so the two moves compound to 21%, not 20%. Rearranged, the formula also gives a shortcut for the ending figure itself: new = old × (1 + increase ⁄ 100), the same statement solved for new instead of for the percentage.
- Enter the starting figure into Old value — the wage, price, or count before it grew.
- Enter the larger, later figure into New (larger) value.
- Read Percentage increase for the growth expressed as a percent of Old value, always reported as zero or positive.
- If New (larger) value turns out smaller than Old value, the sheet flags the input rather than returning a negative number — this page runs one direction by design.
Worked example — a freelancer's rate climbs from $50 to $75
A freelance designer charges an old rate of $50 an hour and lands a new client willing to pay $75 an hour. Percentage increase runs the growth against the starting rate: (75 − 50) ⁄ 50 × 100 = 25 ⁄ 50 × 100 = 50%. The $25 gained is measured entirely against the $50 the designer used to charge, which is why the jump reads as a full half again, not merely as '$25 more.'
Because the page only runs forward, the same two figures cannot be typed the other way to test a pay cut — entering $75 as Old value and $50 as New (larger) value trips the built-in check and asks for a decrease calculation instead, keeping this reading unambiguously a raise.
Questions
Why does this page insist that the new value be larger?
Because percentage increase is the always-positive half of percentage change, built for situations that already carry a known direction — a raise, a price hike, a year's growth. Typing the smaller figure into New (larger) value trips a check rather than silently returning a negative or a nonsensical result, which keeps the sign from ever being misread.
How is percentage increase different from percentage change?
Percentage change accepts either direction and reports a signed answer — a fall becomes a negative percentage automatically. Percentage increase enforces one direction, requires new to be at least old, and always reports a non-negative figure, which suits contexts like wage raises or population growth where the direction is already known and a stray minus sign would only cause confusion.
Why does going from 20 to 100 give a 400% increase, not 500%?
Because the old value, 20, is the 100% baseline being measured from, not counted a second time. The new value, 100, is five times the old one, so the growth on top of that original 100% is (100 − 20) ⁄ 20 × 100 = 400%. Add the growth back to the baseline and 100% + 400% = 500%, which is why the new figure equals 5 × old even though the increase itself reads 400%.
Do two 10% increases in a row add up to a 20% increase?
No — each increase is computed on the value the previous one produced, not on the original figure. A value raised by 10% becomes 1.10 times itself; raised by 10% again it becomes 1.10 × 1.10 = 1.21 times the original, a 21% total increase, not 20%. Chained percentage increases compound rather than sum, which is the same arithmetic behind compound interest.
Can Old value be zero?
No — Old value sits in the denominator of (new − old) ⁄ old × 100, and dividing by zero has no defined result. A quantity that starts at nothing has no base to measure growth against, so this sheet requires Old value to be a positive number rather than returning an infinite or fabricated percentage.
What if Old value and New (larger) value are exactly equal?
The result is a 0% increase — the baseline case, since (50 − 50) ⁄ 50 × 100 = 0 for any matching pair. Nothing grew, so the formula correctly reports nothing to measure, rather than treating an unchanged figure as either a rise or a fall.