What is the percentage change from 50 to 75?

The change is +50%. Calculation: ((75-50)/50) × 100 = 50% increase.

How do I calculate percent change in Excel?

Use formula: =(New-Old)/Old*100 or format as percentage: =(New-Old)/Old then apply % format.

What is the percentage change from 80 to 60?

The change is -25%. Calculation: ((60-80)/80) × 100 = -25% (a decrease).

Why does order matter in percentage change?

Because the denominator (base) must be the original value. Swapping gives a different result: 50→75 is +50%, but 75→50 is -33.3%.

Is percentage change the same as growth rate?

For a single period, yes. Growth rate usually refers to percentage change over time, often compounded.

What if the old value is negative?

The formula still works mathematically, but interpretation becomes complex. Going from -50 to -25 shows +50% (moving toward zero).

What does -100% change mean?

A -100% change means the value has dropped to zero. You cannot decrease by more than 100% (would imply negative values).

How do I calculate year-over-year change?

Use this formula with the previous year as 'Old' and current year as 'New'. Result shows annual growth or decline.

What is the change from 0 to 100?

This is undefined mathematically (division by zero). Any change from zero is infinite in percentage terms.

Can percentage change exceed 100%?

Yes, for increases. A change from 20 to 100 is +400%. However, decreases cannot exceed 100%.

How do I compare two percentage changes?

Compare them directly if they use the same base period. Otherwise, convert to the same timeframe or use index numbers.

What is the difference between absolute and relative change?

Absolute change is the raw difference (New - Old). Relative (percentage) change is the difference as a proportion of the original.

Percentage Change Calculator | Percent Increase/Decrease

Whether you're comparing this month's sales to last month's, tracking a raise in your paycheck, or figuring out how far a stock has moved, a percentage change calculator answers the same question every time: how big was the swing, expressed as a percent? Enter your starting and ending numbers and the tool instantly returns the percentage increase or percentage decrease between them. Below, you'll find the formula broken down step by step, worked examples with negative numbers, and the real-world math — from population growth rate to compound interest — that makes this kind of calculation one of the most useful things you can do with two numbers.

What Is a Percentage Change Calculator?

At its core, a percentage change calculator applies a single piece of mathematics: it takes two numbers and expresses the gap between them as a percent rather than a flat amount. This differs from simply subtracting one number from another, because percentage change accounts for scale — a $10 increase means far more to a $50 budget than to a $5,000 one. That's why the calculator is used across finance, business, economics, and statistics, and in science and mathematics classrooms, whenever people need to compare change relative to a starting point rather than as a raw number. The same relationship can be written as a decimal or a percent — the calculator just automates that ratio-to-percent conversion for you. Some sites call this a percent change calculator instead of a percentage change calculator; they're the same tool under two names.

The Percentage Change Formula: How to Calculate It

The percentage change formula — also written as the percent change formula — compares how far a number has moved relative to where it started:

$$ \text{Percentage Change} = \frac{V_2 - V_1}{|V_1|} \times 100 $$

Here, V₁ is your original value and V₂ is your final value. Subtract V₁ from V₂, divide by its absolute value, then multiply by 100. A positive result is a percentage increase; a negative one is a percentage decrease.

Original Value, Final Value, and New Value

Every percent change calculation starts with two numbers: a starting number and an ending number, sometimes labeled V₁ and V₂. Order matters — always subtract the first from the second, never the reverse, or the positive and negative signs flip and describe the wrong direction of change.

Handling Negative Numbers and Absolute Value

The denominator's absolute value exists specifically for negative numbers. Without it, dividing by a negative initial value would flip the sign of the answer and turn a real increase into a reported decrease. Absolute value simply means treating a number as its distance from zero, whether it's a positive number or a negative number — mathematically, this is sometimes called the modulus of a number.

V₁ (Start)	V₂ (End)	Result (% Change)
40	52	+30% (increase)
-18	18	+200% (increase)
-30	-45	-50% (decrease)

Here's how to calculate percentage change step by step, going from 3.50 to 2.625:

Take the difference: 2.625 − 3.50 = −0.875
Divide by |V₁|: −0.875 ÷ 3.50 = −0.25
Multiply by 100: −0.25 × 100 = −25% change, a 25% decrease

Percentage Change vs. Percentage Difference

Percentage change and percentage difference are often confused, but they're not interchangeable. Percentage change measures movement from one specific value to another, so the order matters and the starting point is always the reference. A difference metric instead compares two values without treating either as the "before," dividing by their average — which is why percent difference is always positive, while percentage change can be positive or negative depending on direction.

Metric	Formula	Can Be Negative?
Directional (this calculator)	(V₂ − V₁) / \|V₁\| × 100	Yes — shows increase or decrease
Symmetric (difference-based)	\|V₁ − V₂\| / ((V₁ + V₂)/2) × 100	No — always positive

Percent Error and Margin of Difference

A related idea is percent error, used when comparing a measured or estimated value to a true value rather than tracking change over time — common in science and lab work. It's calculated the same way as percentage change but framed around accuracy: how large is the margin between what you measured and what's actually correct, expressed as a percent of the true value?

Percent Increase vs. Percent Decrease

A percent increase always reports the final number as larger than where it started, while a percent decrease reports it as smaller — both use the same underlying change calculator formula, but each fixes the direction in advance so the result is shown as a plain positive percentage rather than a signed one. The calculator above handles both directions automatically: a positive result means an increase, a negative result means a decrease.

Percentage Point vs. Percentage Change

A percentage point is not the same thing as a percent. If a discount rate moves from 10% to 15%, that's a 5 percentage point jump — but a 50% percentage change, since 5 is half of the original 10. Mixing up the two is one of the most common errors in financial reporting.

Percent change is also closely tied to basic percent conversions, since every result can be expressed as a decimal before it's turned into the percent you see in the final answer:

Decimal to percent
Percent to decimal
Fraction to percent
Percent to fraction

Real-World Uses: Population Growth Rate, Finance, and Everyday Math

Percent change shows up constantly outside the classroom. A discount at checkout, the tip you leave on a restaurant bill, a salary raise, a swing in stock prices, or economic indicators like inflation and VAT are all percentage changes in disguise. The same formula drives compound interest projections, mortgage payment comparisons, retirement income planning, and time value of money calculations — anywhere interest rates or an investment's returns need to be measured as a rate of change rather than a flat dollar amount. Sales tax works in reverse — a fixed percentage added to a price rather than a change between two values — but the underlying percent math is identical.

Population Growth Rate

Suppose a city's population grows from 180,000 citizens to 207,000 over a decade. Applying the formula: (207,000 − 180,000) ÷ 180,000 × 100 = 15%. That 15% reflects how much the city expanded over that period — the same calculation you'd use for US population figures, a company's revenue, or a lab measurement.

Percent Change in Everyday Life

The same math appears in algebra class, chemistry lab reports, and physics experiments, wherever a measured value needs to be compared against an expected one. A student calculating how much a chemical's temperature rose during a reaction, or a business tracking its numbers quarter over quarter, is running the identical calculation — only the numbers and the units change.

Whatever the context — a raise, a lab result, or a population estimate — the calculator above gives you an exact, correctly-signed answer in seconds, without you needing to memorize the formula or worry about which value goes in the denominator. Now you know exactly how to calculate percent change by hand, or you can just let the calculator do it.

Frequently Asked Questions

Q.What is the percentage change from 50 to 75?: The change is +50%. Calculation: ((75-50)/50) × 100 = 50% increase.
Q.How do I calculate percent change in Excel?: Use formula: =(New-Old)/Old*100 or format as percentage: =(New-Old)/Old then apply % format.
Q.What is the percentage change from 80 to 60?: The change is -25%. Calculation: ((60-80)/80) × 100 = -25% (a decrease).
Q.Why does order matter in percentage change?: Because the denominator (base) must be the original value. Swapping gives a different result: 50→75 is +50%, but 75→50 is -33.3%.
Q.Is percentage change the same as growth rate?: For a single period, yes. Growth rate usually refers to percentage change over time, often compounded.
Q.What if the old value is negative?: The formula still works mathematically, but interpretation becomes complex. Going from -50 to -25 shows +50% (moving toward zero).
Q.What does -100% change mean?: A -100% change means the value has dropped to zero. You cannot decrease by more than 100% (would imply negative values).
Q.How do I calculate year-over-year change?: Use this formula with the previous year as 'Old' and current year as 'New'. Result shows annual growth or decline.
Q.What is the change from 0 to 100?: This is undefined mathematically (division by zero). Any change from zero is infinite in percentage terms.
Q.Can percentage change exceed 100%?: Yes, for increases. A change from 20 to 100 is +400%. However, decreases cannot exceed 100%.
Q.How do I compare two percentage changes?: Compare them directly if they use the same base period. Otherwise, convert to the same timeframe or use index numbers.
Q.What is the difference between absolute and relative change?: Absolute change is the raw difference (New - Old). Relative (percentage) change is the difference as a proportion of the original.