How do you calculate percentage change?

Percentage change = ((New Value - Old Value) / Old Value) x 100. The result is positive for an increase and negative for a decrease. For example, if a price rises from $80 to $100: (100 - 80) / 80 x 100 = +25%. If it falls from $100 to $75: (75 - 100) / 100 x 100 = -25%. The old value (the original, starting, or baseline value) always goes in the denominator. A common mistake is to use the new value as the denominator, which gives a different result. Common real-world applications: (1) Price changes: a product rising from $40 to $52 = +30% increase. (2) Investment returns: portfolio growing from $10,000 to $13,500 = +35% return. (3) Population growth: city population from 500,000 to 620,000 = +24% growth. (4) Weight loss: body weight from 90kg to 81kg = -10% reduction. (5) Revenue decline: sales from $250,000 to $200,000 = -20% drop.

What is the difference between percentage change and percentage point change?

Percentage change and percentage point change are two completely different measures that are frequently confused, especially in finance, economics, and statistics reporting. A percentage change tells you the relative change compared to the starting value: if an interest rate rises from 2% to 3%, that is a 50% increase (1 / 2 x 100 = 50%). A percentage point change is simply the arithmetic difference between two percentage figures: 3% - 2% = 1 percentage point. The distinction matters enormously in context. A politician saying unemployment fell from 8% to 6% might describe it as a 2 percentage point fall (arithmetic), or a 25% reduction (relative). Both are mathematically correct but give very different impressions. Key rules for clarity: (1) Use percentage points when comparing two rates or proportions expressed as percentages. (2) Use percentage change when describing relative growth or decline. (3) Always specify which you mean in written reports to avoid ambiguity. (4) In finance, interest rate moves are almost always quoted in percentage points or basis points (1 basis point = 0.01 percentage points). (5) In science and medicine, absolute risk changes are expressed in percentage points; relative risk changes use percentage change.

Why can't the old value be zero?

Percentage change requires dividing by the old value, and division by zero is mathematically undefined — you cannot calculate how much something has changed relative to nothing. If a company had zero revenue last year and $100,000 this year, saying revenue increased by infinity percent is meaningless in practice. This situation comes up more often than you might expect: (1) A startup reporting its first month of sales compared to a pre-launch period of zero. (2) A product with zero defects in one period compared to a subsequent period. (3) A new country recording its first year of GDP. In these cases, the standard approach is to report the absolute change (e.g. revenue increased by $100,000) rather than a percentage change, since the percentage is undefined or meaningless. Some analysts use a convention of treating the result as not applicable (N/A) or as a special symbol. This calculator correctly flags the zero denominator case and does not produce a result.

What does the multiplier mean?

The multiplier is the ratio of the new value to the old value: multiplier = New / Old. It tells you the new value expressed as a multiple of the original. A multiplier of 1.25 means the new value is 1.25 times the old — equivalent to a +25% change. A multiplier of 0.75 means the new value is 75% of the old — equivalent to a -25% change. Multipliers are particularly useful for chaining percentage changes: if something increases by 20% and then by 10%, the combined multiplier is 1.20 x 1.10 = 1.32, meaning a total increase of +32% — NOT 30% (the common mistake of simply adding percentages). Key multiplier benchmarks: (1) Multiplier of 2.0 = doubled = +100% increase. (2) Multiplier of 1.5 = grown by half = +50% increase. (3) Multiplier of 1.0 = no change = 0%. (4) Multiplier of 0.5 = halved = -50% decrease. (5) Multiplier of 0.0 = reduced to zero = -100% decrease.

How is percentage change used in finance and investing?

Percentage change is one of the most fundamental measures in finance because it enables comparison of performance across assets, time periods, and portfolios of different sizes. A $500 gain on a $1,000 investment (50% return) is far more impressive than the same $500 gain on a $100,000 investment (0.5% return). Without percentage change, raw numbers are often meaningless for comparison. Common finance applications: (1) Investment returns: (ending value - starting value) / starting value x 100, e.g. buying a share at $40 and selling at $55 = +37.5% return. (2) Compound Annual Growth Rate (CAGR): the smoothed annual percentage change over multiple years. (3) Earnings per share (EPS) growth: measuring year-over-year profit improvement. (4) Price-to-earnings ratio changes: tracking valuation expansion or contraction. (5) Currency appreciation/depreciation: GBP/USD moving from 1.25 to 1.30 = GBP appreciated by 4%. (6) Inflation measurement: the Consumer Price Index (CPI) percentage change year-over-year is the headline inflation figure. Always distinguish between nominal returns (raw percentage change) and real returns (adjusted for inflation), as they can differ significantly over longer periods.

Percentage Change Calculator — Increase, Decrease & Multiplier

This Percentage Change Calculator finds the percentage increase or decrease between any two numbers. Enter the old (original) value and the new (current) value, and the calculator computes the percentage change, the absolute change amount, and the multiplier. A positive result means an increase; a n...

% CHANGE

Old Value (original)

↓

New Value (current)

80 → 100

+25%

(100 − 80) ÷ 80 × 100 = +25%

CHANGE AMT

+20

MULTIPLIER

1.25×

DIRECTION

▲ Up

QUICK EXAMPLES

LIVE DIAGRAM

PERCENTAGE CHANGE

+25%

CHANGE AMOUNT

+20

MULTIPLIER

1.25×

DIRECTION

▲ Increase

OLD vs NEW

Old

New

100

CHANGE MAGNITUDE (capped at ±100% for display)

−100%0+100%

OLD VALUE

NEW VALUE

100

CHANGE AMT

+20

MULTIPLIER

1.25×

Live diagram · updates as you type

Created with❤️byeaglecalculator.com

WHAT NEW VALUES GIVE COMMON % CHANGES FROM 80?

OLD VALUE: 80 — YOUR CHANGE: +25%

% CHANGE	NEW VALUE	CHANGE AMT	MEANING
-50%	40	-40	Half the original
-25%	60	-20	Down a quarter
-10%	72	-8	Down 10%
+0%	80	+0	No change
+10%	88	+8	Up 10%
+25% ← yours	100	+20	Up a quarter
+50%	120	+40	Up half
+100%	160	+80	Doubled

HOW TO USE

1
Enter the old value — this is the original, starting, or baseline number. It goes in the denominator of the formula, so it cannot be zero.
2
Enter the new value — this is the current, final, or updated number you are comparing against the old value.
3
The percentage change appears instantly — positive for an increase, negative for a decrease. The formula is shown below the result.
4
Review the reference table to see what new values correspond to common benchmark changes from your old value. Your actual result is highlighted.
5
Use the quick example buttons to load common scenarios — price increases, revenue drops, investment returns — and see the calculator in action.

WORKED EXAMPLE

Example 1: Old = 80, New = 100. Change = (100 - 80) / 80 x 100 = +25%. Multiplier: 1.25x. Example 2: Old = 100, New = 75. Change = (75 - 100) / 100 x 100 = -25%. Multiplier: 0.75x. Example 3: Old = 200, New = 250. Change = (250 - 200) / 200 x 100 = +25%. Example 4: Old = 1500, New = 1200. Change = (1200 - 1500) / 1500 x 100 = -20%. Multiplier: 0.8x.

REFERENCE FORMULAS

FORMULA REFERENCE TABLE

NAME	FORMULA	DESCRIPTION
Percentage Change	% Change = ((New - Old) / Old) x 100	Positive = increase, negative = decrease. Old value cannot be zero
Change Amount	Change Amount = New - Old	The absolute difference between new and old values
Multiplier	Multiplier = New / Old	New value as a multiple of old — 1.25x = 25% increase, 0.75x = 25% decrease
New from % Change	New = Old x (1 + Change% / 100)	Find the new value that results from a given percentage change
Old from % Change	Old = New / (1 + Change% / 100)	Find the original value given the new value and the percentage change

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Last updated: April 25, 2026 · Formula verified by EagleCalculator team · Eagle-eyed accuracy for every calculation.