Percentage change answers one question: relative to where it started, how far did a value move, and in which direction? Unlike a plain difference, it scales the move by the starting size, so a $5 rise on a $20 item (+25%) is not confused with a $5 rise on a $2,000 item (+0.25%). This calculator returns a signed result — a plus for growth, a minus for decline — so you never have to choose between an “increase” and a “decrease” tool before you know the answer.
How to use the percentage change calculator
- Enter the starting value — the old, earlier or reference number.
- Enter the ending value — the new or later number.
- Tick the checkbox if both numbers are already percentages (interest rates, poll results, pass rates) to see the change in percentage points as well.
- Read the signed result on the tape. Below it you’ll find the raw change, the growth factor and the change needed to return to the starting value.
Percentage change formula
The order matters. The starting value goes in the denominator because it is the base you compare against. Swap the two numbers and you get a different answer, which is why “from” and “to” must be clear before you calculate.
Worked example
A coffee shop sold 80 cold brews on Monday and 92 on Tuesday.
Change: 92 − 80 = 12 more drinks
Relative change: 12 ÷ 80 = 0.15
Percentage change: 0.15 × 100 = +15%
Going back: if Wednesday drops to 80 again, that is (80 − 92) ÷ 92 × 100 ≈ −13.04%
The two moves are the same 12 drinks, yet their percentages differ because each one is measured from a different base. That asymmetry is normal, not a rounding error.
Reading the sign
- Positive (+15%): the value grew. A growth factor above 1 says the same thing — 92 ÷ 80 = 1.15.
- Negative (−20%): the value shrank. The growth factor is below 1, for example 0.8.
- Zero: the two values are equal.
- Below −100% is impossible for positive quantities. A positive number cannot fall by more than all of itself without crossing zero.
When the starting value is negative
Profit and loss figures, temperatures and account balances can start below zero. Dividing by the plain (negative) starting value would flip the sign and report an improvement as a decline, so the calculator divides by the absolute value of the start. A quarterly loss narrowing from −$50,000 to −$20,000 shows as +60%: the number moved up. Even so, percentages across zero are fragile, and many analysts report them as “not meaningful”. When the sign of the value changes, state the dollar change too.
Percentage change or percentage points?
When the values are themselves percentages, two different statements are both correct:
| Rate moves from | Percentage-point change | Percentage change |
|---|---|---|
| 4% → 5% | +1 pp | +25% |
| 40% → 50% | +10 pp | +25% |
| 12% → 9% | −3 pp | −25% |
News reports about interest rates, unemployment and polls usually quote percentage points because they are less dramatic and easier to compare. Use the checkbox to get both.
Which percentage tool do you need?
- Use this page when you have an old and a new value and want a single signed answer.
- To raise a number by a percentage or recover the value before a raise, use the percentage increase calculator.
- For discounts, markdowns and drops, the percentage decrease calculator works in the other direction.
- If neither value is the “original” — two stores, two lab samples — the percentage difference calculator compares them symmetrically.
- For growth across many years, the CAGR calculator turns total change into an average yearly rate.
Frequently asked questions
What is the formula for percentage change?
Percentage change = (new − old) ÷ |old| × 100. A result above zero is an increase and a result below zero is a decrease. Going from 80 to 92 gives (92 − 80) ÷ 80 × 100 = +15%.
Why can't I calculate a percentage change from zero?
The formula divides by the starting value, and division by zero has no answer. Any growth from nothing would be infinitely large in relative terms, so report the plain difference instead, for example "up 45 units from zero".
Is a change from 92 back to 80 also 15%?
No. The return trip is measured against 92, the new starting point, so it is (80 − 92) ÷ 92 × 100 ≈ −13.04%. The calculator shows this as the change needed to go back.
How do I handle a negative starting value?
Divide by the absolute value of the starting number so the sign of the answer still matches the direction of the move. A loss shrinking from −50 to −20 is +60%, an improvement. Treat such results with care and report the raw change alongside them.
What is the difference between percent change and percentage points?
Percentage points are the plain gap between two percentages, while percent change is that gap relative to the starting percentage. An approval rating moving from 40% to 50% rose 10 percentage points, which is a 25% increase.