Rechnerpilot Calculator

Percentage Change

Calculate the percentage change between two values — determine increase, decrease, new or old value instantly for free.

Available

Inputs

Enter values

Live

Calculate changeCompare old and new value as a percentage

Old value

The previous or original reference value.

New value

The current, new or known final value.

Load example

For illustration only – your own calculation is what counts.

Explanation

How Percentage Change works

The percentage change calculator compares two values: an old base value and a new value.

The result shows whether the new value has risen, fallen or remained unchanged. Additionally, the absolute difference is displayed.

The calculator can also compute the new value from an old value and a change, or reverse-calculate the old value from a new value and a change.

Percentage change is one of the most important tools in business and statistics. It makes changes comparable regardless of the absolute size of the base values. An increase of 10 EUR represents a 10% gain on a base of 100 EUR, but only 1% on a base of 1,000 EUR.

In reporting, percentage change is frequently used for economic indicators: GDP growth, inflation rate, revenue development or stock prices. The reference value (old value) is decisive — a 50% increase followed by a 50% decrease does not return to the starting value.

Percentage change(neu - alt) / alt x 100

The difference between new and old value is related to the old value.

Absolute changeneu - alt

The absolute change shows the difference as a number.

New valuenew = old x (1 + change / 100)

Positive changes increase the old value, negative changes decrease it.

Old value (reverse)old = new / (1 + change / 100)

When the new value and change are known, divide by the change factor.

Change factorFactor = new / old

The change factor shows the ratio directly: a factor of 1.15 means 15% increase, a factor of 0.8 means 20% decrease.

Knowledge

Distinguishing absolute and relative change

The absolute difference shows the change as a number. The percentage change relates this difference to the old value.

From 200 to 230, the absolute difference is 30. Relative to the old value of 200, that is 15%. For a decrease, the percentage becomes negative, interpreted as a decline or reduction.

Comparison: new value minus old value, divided by old value.
New value: old value times the change factor.
Old value (reverse): new value divided by the change factor.

Practice

Practical examples

For illustration only – your own calculation is what counts.

Compare a price increase

From 200 to 230, the calculator shows the increase as a percentage and as an absolute difference.

Result: The increase is 15%, absolute 30.

Calculate a decline

From 150 to 120, the percentage decrease becomes visible.

Result: The decrease is 20%, absolute -30.

Compare a metric

With old and new measured values, you immediately see the percentage change.

Result: The increase is 25%.

Calculate new value from a change

From an old value and a change of 15%, the new value is calculated.

Result: The new value is 230, absolute plus 30.

Find old value (reverse)

When the new value and the percentage change are known, the original old value is reconstructed.

Result: The old value was 200.

Notes

Common mistakes

Choosing the wrong reference value
The percentage change always refers to the old value. If you accidentally use the new value as the reference, you get an incorrect result. From 100 to 150 is +50%, but from 150 to 100 is -33.3%.
Always use the earlier or base value as the reference: (new - old) / old x 100.
Confusing absolute and relative change
An absolute change of 10 EUR can mean 1% or 50% relative change depending on the base value. Both figures are correct but not interchangeable.
Always specify whether you mean the absolute difference (in EUR) or the relative change (in percent).
Ignoring asymmetry in up and down movements
After a 25% increase, a decrease of 20% (not 25%) is sufficient to return to the starting value. This is because the reference value changes.
Reverse calculation with factor: 125 / 1.25 = 100. Or: decrease = 1 - (1/1.25) = 20%.
Stating percentage points instead of percentage change
When a rate rises from 5% to 8%, that is an increase of 3 percentage points, but a percentage change of 60%. Both statements are correct but describe different things.
Use percentage points for the difference between percentage figures, and percentage change for the ratio.
Trying to calculate a change from a starting value of 0
If the old value is 0, the percentage change is mathematically undefined (division by 0). In such cases, a different metric must be used.
With a starting value of 0, state the absolute difference instead or choose a different reference value.

FAQ

Frequently asked questions

How do you calculate a percentage change?

The new value minus the old value is divided by the old value and multiplied by 100.

What does a negative change mean?

When the new value is smaller than the old value, the change is a decrease.

Why can the old value not be 0?

A percentage change requires a reference value. With 0, the division is undefined.

What is the difference between absolute and percentage change?

The absolute change is new value minus old value. The percentage change relates this difference to the old value.

Can a percentage change be negative?

Yes. A negative percentage describes a decrease. -20% means the new value is 20% below the old value.

How do you calculate the new value from a change?

Multiply the old value by 1 plus the change divided by 100. For 15%, the factor is 1.15; for -20%, it is 0.8.

How do you reverse-calculate the old value?

Divide the new value by the change factor. The factor is 1 plus the change divided by 100.

Why is -100% ambiguous when reversing the old value?

At -100%, the new value would be 0. From 0, no unique old value can be reconstructed.

Are percentage points the same as percentage change?

No. Percentage points describe the difference between two percentage figures. Percentage change relates two values to each other.

Can a percentage change exceed 100%?

Yes. An increase from 100 to 250 corresponds to a gain of 150%. That means the new value is 2.5 times the old one. For decreases, however, -100% is the maximum since the value then drops to 0.

Limits

Limitations

Old value must not be 0: With a starting value of 0, the percentage change is mathematically undefined. The calculator does not produce a result in this case.
No time series analysis: The calculator compares exactly two values. For time series with multiple data points (e.g. monthly change rates), a statistics tool is more suitable.
No annualisation: The calculator does not compute a compound annual growth rate (CAGR) from multiple periods. For average growth over several years, use a compound interest calculator.
Simple change only: Cumulative or chained changes (e.g. +10% in year one, -5% in year two) must be calculated step by step.

Sources

Sources and references

Statistisches Bundesamt — Methodische GrundlagenStatistisches Bundesamt (Destatis)
The Federal Statistical Office defines standards for the calculation and presentation of percentage changes in official statistics.
View sourceRetrieved: 06/15/2025 · Verified on: 07/23/2026 · Primary source
Deutsche Bundesbank — Zeitreihen und VeränderungsratenDeutsche Bundesbank
The Bundesbank calculates change rates for economic indicators and documents the methodological foundations of percentage change.
View sourceRetrieved: 06/15/2025 · Verified on: 07/23/2026 · Primary source
Kernlehrplan Mathematik NRW — Prozentuale VeränderungMinisterium für Schule und Bildung NRW
The core curriculum for mathematics covers percentage change as an extension of percentage calculation in grades 7/8.
View sourceRetrieved: 06/15/2025 · Verified on: 07/23/2026
ifo Institut — Konjunkturberichte mit Veränderungsratenifo Institut
The ifo Institute uses percentage changes as the standard measure in economic reports, business climate indices and economic forecasts.
View sourceRetrieved: 06/15/2025 · Verified on: 07/23/2026

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