Percent Increase Calculator

Background.

A percent increase calculator answers one of the most frequently typed questions in a search box: by what percentage did this go up? Enter the old value and the new value and the page returns two numbers — the percent increase, and the plain absolute change in whatever units you're working in. Type a salary before and after a raise, a rent before and after a renewal, a population count from one census to the next, or a stock price at open and close, and the calculator does the division for you, using arbitrary-precision decimal arithmetic so that a figure like $4,680 on a $52,000 base returns exactly 9%, not 8.999999999999998%.

This page exists as a deliberately narrow, single-purpose tool, and that is a feature rather than a limitation. Quanta already ships a general percentage-change calculator that reports a signed percent change, the absolute change, and a symmetric percent-difference figure side by side — useful when you need all three, or when neither of your two numbers is obviously the reference point. "Percent increase" is a different kind of question. It is asked by someone who already knows which number came first and which number came after, wants the growth expressed as a single figure, and does not want to interpret a sign convention or a third column they didn't ask for. That is the entire reason this page is separate from the general tool: percent increase and percent decrease are, by search volume, two of the highest-traffic percentage queries on the internet, distinct enough from the generic "percentage change" phrase that a dedicated landing page serves the reader faster.

The formula is simple but the mistakes people make with it are not. The most common one is reversing the base: going from $80 to $100 is a 25% increase, but going back from $100 to $80 is only a 20% decrease, even though the dollar amount ($20) is identical both ways. That asymmetry surprises almost everyone the first time they hit it, because our intuition treats percentages as if they were fixed units like inches or grams, when in fact a percentage is only meaningful relative to whichever number sits in the denominator. This calculator always divides by the old value — the value you started with — which is the standard convention used in finance, retail, payroll, and government statistics reporting alike.

The second common mistake is confusing a percent increase with a percentage-point increase. If a commission rate moves from 4% to 5%, that is a 1 percentage-point increase but a 25% percent increase (because 1 ÷ 4 × 100 = 25). Confusing the two is not a rounding error — it changes the reported number by an order of magnitude, and it is one of the most frequently cited numeracy mistakes in financial and political journalism. The FAQ section below walks through this distinction with worked numbers so you can catch it in your own work before it becomes a wrong headline or a wrong invoice.

Because the formula divides by the old value, an old value of exactly zero makes the calculation mathematically undefined — you cannot express growth from nothing as a percentage of nothing. Quanta's engine throws a clear error in that case rather than silently returning Infinity or a misleading zero, the same way a spreadsheet would return a #DIV/0! error rather than a fabricated number. If you are genuinely trying to describe something that grew from a starting value of zero, report the raw numbers instead of a percentage, or use a logarithmic or absolute measure that tolerates a zero baseline. Negative starting values are supported correctly using the absolute value of the old value in the denominator, matching the convention used across every other percentage tool on this site.

Below the calculator you'll find the full formula derivation, a hand-verified worked example using a real salary raise, and eight frequently asked questions covering percentage points, negative results, reversing the base, and when to reach for the more general percentage-change tool instead of this one.

What is percent increase calculator?

Percent increase is the directional, signed measure of how much a value has grown, expressed as a percentage of its original value. Formally: percentIncrease = (newValue − oldValue) ÷ |oldValue| × 100. It is the same underlying relative-difference arithmetic taught under Common Core State Standard 7.RP.A.3, which explicitly names "percent increase and decrease" alongside markups, markdowns, and simple interest as applications of proportional reasoning. A percent increase calculation always needs two ordered numbers — an old (earlier, starting, or baseline) value and a new (later, ending, or resulting) value — because the percentage is only meaningful once you know which number is being used as the point of reference. Unlike a plain difference, which is measured in the same units as the original quantity (dollars, people, degrees), a percent increase is dimensionless: a 10% raise means the same relative thing whether the salary is $30,000 or $300,000, even though the dollar amounts involved are ten times apart. That scale-independence is exactly why percentages are the preferred way to compare growth across quantities of very different sizes — comparing a country's population growth to a city's, or a small company's revenue growth to a large one's, only makes sense in percentage terms, because the absolute numbers are not comparable on their own.

How to use this calculator.

1. 01Enter the old value — the starting number, before the increase happened.
2. 02Enter the new value — the ending number, after the increase happened.
3. 03Read the percent increase. A positive number means the value grew by that percentage relative to the old value.
4. 04Read the absolute change for the plain dollar-or-unit difference between the two numbers, useful when you need to report both figures side by side.
5. 05If the percent increase comes back negative, the value actually fell rather than rose — switch to the percent-decrease calculator for a page framed around that direction, or use the general percentage-change tool if you want both directions handled identically.
6. 06Double-check which number you entered as "old" — swapping old and new does not just flip the sign of the result, it also changes the denominator, so the magnitude changes too.

The formula.

The formula has two parts. The absolute change is simply newValue minus oldValue — a plain subtraction that keeps the original units (dollars, people, degrees, whatever you entered). The percent increase converts that same difference into a dimensionless ratio: divide the absolute change by the absolute value of the old value, then multiply by 100 to express it as a percentage out of one hundred.

Using the absolute value of the old value in the denominator — rather than the old value itself — matters only when the old value is negative. Without it, a move from −50 to −20 (the negative quantity shrinking toward zero, generally a good thing if the quantity is debt or a temperature deviation) would compute as (−20 − (−50)) ÷ (−50) × 100 = 30 ÷ −50 × 100 = −60%, which reads as a decrease even though the underlying situation improved. Taking the absolute value of the denominator fixes the sign so that a shrinking negative quantity correctly reports as a positive percent increase: (−20 − (−50)) ÷ |−50| × 100 = 30 ÷ 50 × 100 = 60%.

Because the formula divides by the old value, oldValue = 0 is the one input this calculator refuses. There is no percentage you can honestly attach to "grew from nothing," because any nonzero new value divided by zero is undefined, not infinite in any useful sense, and definitely not zero. If you hit that case, report the raw before/after numbers instead of forcing them through a percentage formula that cannot express the situation.

One more property worth internalizing: percent increase and percent decrease are not mirror images of the same magnitude when applied in sequence. A value that increases 25% and then decreases 25% does not return to its starting point — because the second percentage is calculated against the new, larger base. $100 increased by 25% is $125; $125 decreased by 25% is $93.75, not $100. This is the same asymmetry that makes recovering from a loss always require a proportionally larger gain than the loss itself, and it's covered in more depth in the FAQ section below.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Common Core State Standards for Mathematics, Grade 7, Ratios & Proportional Relationships, Standard 7.RP.A.3 — proportional relationships applied to multistep ratio and percent problems, explicitly naming percent increase and decrease.
2. [2]Common Core State Standards for Mathematics, Grade 6, Ratios & Proportional Relationships, Standard 6.RP.A.3(c) — finding a percent of a quantity as a rate per 100, the foundational skill percent increase builds on.
3. [3]NIST Guide to the SI, Special Publication 811, §7.10.2 — rules and conventions for expressing relative differences as dimensionless percentages.
4. [4]Board of Governors of the Federal Reserve System — FAQ explaining the distinction between percentage points and percent change when describing interest-rate movements.
5. [5]NIST Digital Library of Mathematical Functions, §4.2 — formal definitions of logarithm, exponential, and power relationships underlying ratio and proportional-growth arithmetic.