Percentage Change Calculator

About this Percentage Change Calculator

The Percentage Change Calculator compares a new value with an original value and expresses the difference as a percentage of the original. It is useful for prices, traffic, revenue, scores, measurements and many before-versus-after comparisons.

Percentage change is calculated relative to the original (starting) value, not the new value, which trips people up constantly when comparing a price increase against a later decrease, since going up 50% and then down 50% does not return you to the starting number.

For related tasks, try Percentage Calculator, Ratio Calculator or Investment Return Calculator.

How the calculation works

Percentage change is calculated as (new value − original value) ÷ |original value| × 100. When the original value is zero, a standard percentage change is not defined.

How to use it

1. Enter the original value.
2. Enter the new value.
3. Calculate to see the absolute change and percentage change.

Practical example

If a value rises from 80 to 100, the increase is 20 and the percentage change is 25%.

A price that rises from 50 to 75 has increased by 50%, but if that same 75 later falls back to 50, that is only a 33.3% decrease, not 50%, because the base of the second calculation (75) is larger than the base of the first (50).

Things to double-check

A percentage increase and the percentage decrease needed to reverse it are never equal in magnitude except at 0%; if a value rises by 100%, it must fall by 50%, not 100%, to return to its original level, since the base for the second calculation is now the larger number.

How the change is measured

Percentage change is the difference between the new and old values divided by the old value. If a price goes from 80 to 100, the change is 20 divided by 80, which is a 25 percent increase. If it goes from 100 to 80, the change is minus 20 divided by 100, a 20 percent decrease. The same 20 unit gap gives different percentages because the starting point is different. A positive result means an increase and a negative result a decrease.

Why the order matters

Increases and decreases do not cancel out. A 10 percent rise followed by a 10 percent fall leaves you at 99 percent of the original, because 1.10 times 0.90 is 0.99. After a 50 percent loss you need a 100 percent gain to return to the start, and after a 20 percent loss you need 25 percent. This matters for investments, where a big fall is harder to recover from than it looks. When you describe changes over several periods, multiply the factors instead of adding the percentages.

Percent change versus percentage points

When a quantity that is itself a percentage changes, be precise. A rate rising from 4 percent to 5 percent is a one percentage point change but a 25 percent relative increase. Unemployment, interest rates and market shares are all reported this way. If you are unsure which a writer means, look at the original numbers and apply the formula above yourself. The calculator gives the relative change from the old value.

Edge cases and good practice

The formula fails when the old value is zero, because dividing by zero is undefined, and it can be misleading when the old value is very small, as a rise from 1 to 3 is 200 percent but may be trivial in practice. It also behaves oddly with negative numbers, so describe those changes in plain differences. For growth across many years, use compound annual growth rather than a single total, which shows the equivalent yearly change. Always state the starting and ending values with a percentage so readers can check.

Averaging changes correctly

You cannot average percentage changes by adding them. A 50 percent gain followed by a 50 percent loss averages to zero but leaves you 25 percent down, since 1.5 times 0.5 is 0.75. To find the equivalent steady change, multiply the growth factors and take a root: growth from 100 to 121 over two years is 10 percent a year, because the square root of 1.21 is 1.10. This compound approach is used for investments, population and prices. When you report changes over several periods, state the starting and ending values so readers can check your figures.

Worked example: rent, salary and inflation

A tenant's rent rises from 1,200 to 1,296, a change of 96, which is 8 percent of 1,200. At the same time the tenant's salary rises from 4,000 to 4,300, an increase of 300, or 7.5 percent. If prices rose by 5 percent over the year, the real rise in salary is 1.075 divided by 1.05, which is about 2.4 percent, while the rent rose by about 2.9 percent in real terms. So the tenant is slightly worse off in housing even though the salary rose. Percentage changes make such comparisons clear because they put different amounts on the same scale.

Recovering from a fall

The percentage you need to recover is always larger than the percentage you lost. A 25 percent discount takes a 100 price to 75, and to return to 100 the price must rise by 25 divided by 75, which is 33.3 percent. A 50 percent loss needs a 100 percent gain, and a 10 percent loss needs about 11.1 percent. This asymmetry explains why avoiding large losses matters in investing and why businesses do not give very deep discounts lightly. When you plan a price change, calculate the reverse change so that you know what it takes to get back.

Small bases and zero

Percentage changes can mislead when the starting value is very small. A rise from 0.5 to 1.5 is a 200 percent increase, although the absolute change is only one unit. A change from zero has no percentage at all, since you cannot divide by zero. Reports on new products, early-stage growth and rare events often quote very large percentages that fade as the base grows. If the base is small, give the actual numbers alongside the percentage. If the base is negative, as with profit that moves from a loss to a gain, percentage change loses its meaning and a plain difference is clearer.

Reporting changes properly

State the period and the starting value when you report a change. Year-on-year comparisons remove seasonal effects, while month-to-month changes show the latest direction but can be distorted by the season. If sales rise from 80 in January to 92 in February, that is 15 percent, but compare it with the same months last year before you conclude that business is improving. For long periods, convert the total change into a yearly rate. Use charts with the baseline clearly marked, and avoid axes that exaggerate small changes. Clear reporting builds trust and lets readers check your numbers.

Key terms explained

The old value is the starting amount and the new value the ending amount. The change is the new value minus the old value, and the percentage change divides this by the old value. An increase is positive and a decrease is negative. A percentage point difference is used when comparing two percentages. The growth rate is a percentage change over a period, and year-on-year compares the same period in different years. The compound annual growth rate gives a steady yearly equivalent.

Rules of thumb and quick checks

Percentage change equals new minus old, divided by old, times 100. A 20 percent rise followed by a 20 percent fall leaves you 4 percent lower, since 1.2 times 0.8 is 0.96. To reverse an increase of x percent, you need a decrease of x divided by one plus x. If new over old is 1.15, the rise is 15 percent. Be careful when the old value is zero or very small, and state both values when you report a change.

Frequently asked questions