How to Calculate Percentage Change and Percentage Difference

To calculate percentage change, subtract the original value from the new value, divide by the original value, then multiply by 100. A positive result is a percentage increase; a negative result is a percentage decrease. This single formula handles both directions.

Percentage calculations come up constantly — a salary negotiation, a sale price, a stock return, a grade on a curved exam. Getting the formula wrong by even one step produces a result that looks plausible but is off. A price that goes from $80 to $100 is a 25% increase, not a 20% increase — the two most common answers people give, and only one is correct. The distinction matters in every financial comparison you make.

Use the free Percentage Calculator at RoughTools to calculate percentage change, percentage difference, and percentage of a number instantly — or follow the step-by-step method below.

The Percentage Change Formula

Percentage change and percentage difference are related but distinct calculations. Each has its own formula and applies to different situations.

Percentage change (used when there is a clear "before" and "after"):

Percentage Change = ((New Value − Original Value) / Original Value) × 100

Percentage difference (used when comparing two values with no defined direction):

Percentage Difference = (|V1 − V2| / ((V1 + V2) / 2)) × 100

Percentage of a number (used to find what portion X is of Y):

Percentage = (Part / Whole) × 100

Where:

New Value — the value after the change (the more recent measurement)
Original Value — the starting point before the change occurred
|V1 − V2| — the absolute difference between two values (always positive)
(V1 + V2) / 2 — the average of the two values, used as the reference point
Part / Whole — the specific value divided by the total it belongs to

Worked example: laptop price change

A laptop costs $847 in January. By September, the same model costs $1,124.

Step 1 — Identify new and original values:

Original Value = $847
New Value      = $1,124

Step 2 — Find the difference:

New − Original = 1,124 − 847 = 277

Step 3 — Divide by the original value:

277 / 847 = 0.3270

Step 4 — Multiply by 100:

0.3270 × 100 = 32.70%

The result: the laptop price increased by 32.70% from January to September. If you paid $847 and the item is now $1,124, you saved $277 — not 20% and not 25%, but precisely 32.70% relative to what you originally paid. This is why anchoring on the original price (the denominator) is critical.

How to Calculate Percentage Change Step by Step

Identify your original value and your new value clearly. Before any calculation, label which number is the starting point and which is the ending point. The original value always goes in the denominator — swapping them produces a different and incorrect answer. For a pay raise from $52,400 to $58,700: original = $52,400, new = $58,700.
Subtract the original from the new value. This gives you the raw change — positive if the value increased, negative if it decreased. For the salary example: 58,700 − 52,400 = 6,300. Keep the sign — a negative difference means a decrease and should produce a negative percentage change.
Divide the raw change by the original value. This step converts the raw difference into a fraction of the starting point. For the salary: 6,300 / 52,400 = 0.1202. This is the decimal form of the percentage change, not the final answer yet.
Multiply by 100 to convert to a percentage. Move the decimal point two places to the right: 0.1202 × 100 = 12.02%. A raise from $52,400 to $58,700 is a 12.02% increase — a number you can verify against an employer's stated raise percentage.
Interpret the sign and magnitude. A positive percentage is an increase; negative is a decrease. The magnitude tells you the scale of change relative to the original. A 5% change on a small number is a small absolute difference; a 5% change on a large number is a large absolute difference.
Verify by reversing the calculation. Multiply the original value by (1 + percentage/100) and confirm you get the new value. For the salary: 52,400 × 1.1202 = 58,698.5 ≈ $58,700 (minor rounding). If your verification does not match, you divided by the wrong value in Step 3.

Pro tip: When a price drops, many people instinctively put the new (lower) price in the denominator. This is wrong for percentage change. Always divide by the original starting price, regardless of which is larger. Dividing by the wrong value is the source of nearly all percentage-change errors.

What Is the Difference Between Percentage Change and Percentage Difference?

Percentage change requires a defined "before" and "after." Percentage difference is used when comparing two values where neither is clearly the reference starting point.

If a product's price changed from $63.50 to $79.99, that is a percentage change — the original price is the baseline, and the new price represents movement from it.

If Store A sells the same product for $63.50 and Store B sells it for $79.99, and you want to know how different the prices are, that is a percentage difference. Neither price is "before" or "after" — they are just two current prices. The formula averages the two values to create a neutral reference point:

Percentage Difference = (|79.99 − 63.50| / ((79.99 + 63.50) / 2)) × 100
= (16.49 / (143.49 / 2)) × 100
= (16.49 / 71.745) × 100
= 22.98%

The two store prices differ by 22.98%. Notice this is different from the percentage change from $63.50 to $79.99, which is 26.0%. The choice of denominator — average vs. original — produces two legitimately different answers for two legitimately different questions.

Use percentage change for: before-and-after comparisons, growth rates, price movements, grade changes. Use percentage difference for: side-by-side comparisons with no natural baseline, comparing two measurements of the same thing, expressing how far apart two current values are.

How Do You Find the Percentage of a Number?

To find the percentage of a number, multiply the whole by the percentage divided by 100. The formula is: Part = (Percentage / 100) × Whole.

Three common percentage questions and how to solve each:

"What is 18% of $347?"

Part = (18 / 100) × 347
Part = 0.18 × 347
Part = $62.46

"$62.46 is what percentage of $347?"

Percentage = (62.46 / 347) × 100
Percentage = 0.18 × 100
Percentage = 18%

"$62.46 is 18% of what number?"

Whole = 62.46 / (18 / 100)
Whole = 62.46 / 0.18
Whole = $347

These three questions are inverses of each other — if you know any two values, you can find the third. In practice, the most common application is tip calculation (15% of a $94 restaurant bill = $14.10), sales tax (8.25% of a $247 purchase = $20.38), or grade weighting (a 78 on a test worth 40% of the grade contributes 31.2 points to the total).

The percentage calculator handles all three question types — you specify which value is unknown, enter the other two, and get the result immediately.

How to Calculate Percent Increase and Percent Decrease

Percent increase and percent decrease use the same formula — percentage change — with interpretation based on the sign of the result.

Percent increase: New value is larger than original. Result is positive. Percent decrease: New value is smaller than original. Result is negative.

A common point of confusion: a 50% increase followed by a 50% decrease does not return to the original value. Starting at $200:

50% increase: 200 × 1.50 = $300
50% decrease from $300: 300 × 0.50 = $150

The result is $150 — 25% below the starting $200. This happens because the 50% decrease is applied to a larger base ($300) than the 50% increase was applied to ($200). Percentage changes are multiplicative, not additive. To return to $200 from $300, you need a 33.3% decrease, not a 50% decrease.

This asymmetry has real implications. A stock that falls 40% from $85 to $51 requires a 66.7% gain to return to $85 — not a 40% gain. According to the mathematics of compounding, losses always require a larger percentage gain to recover than the percentage they fell. A 50% loss requires a 100% gain. Understanding this asymmetry helps explain why preventing large drawdowns matters more in investing than maximizing big gains.

Use the discount calculator when applying sequential percentage changes to a price — it handles multi-step discounts and increases without the compounding confusion.

Common Mistakes to Avoid When Calculating Percentage Change

Dividing by the new value instead of the original. The original value — the starting point — is always the denominator. If a salary rises from $48,000 to $54,000, divide by $48,000: change = (6,000 / 48,000) × 100 = 12.5%. Dividing by $54,000 gives 11.1% — technically the answer to a different question ("what percentage of the final value is the change?").
Adding percentage changes together instead of compounding them. A 10% increase followed by a 10% increase is not a 20% increase — it is a 21% increase. Each percentage applies to the new base, not the original. For multi-step changes, multiply the decimal equivalents: 1.10 × 1.10 = 1.21. This mistake appears most often in multi-year growth calculations.
Confusing percentage points with percentage change. If an interest rate rises from 3% to 4%, it increased by 1 percentage point — but that is a 33.3% increase in the rate itself. "A 1% rise" and "a rise of 1 percentage point" are completely different statements. Financial and political reporting conflates these constantly.
Using percentage difference when percentage change is appropriate (or vice versa). If a value changed over time, use percentage change with the original as the denominator. If you are comparing two current, simultaneous values, use percentage difference with the average as the denominator. Applying the wrong formula gives an answer that is technically a number but statistically meaningless.
Forgetting that percentage change is direction-dependent. A 25% increase from $80 to $100 is not the same as a 25% decrease from $100. The 25% increase brings you to $100 (80 × 1.25 = 100). But a 25% decrease from $100 gives $75 (100 × 0.75 = 75), not $80. Percentage changes are always relative to the value they are applied to, which changes with each step.

Frequently Asked Questions

What is the easiest way to calculate percentage change in my head? Divide the difference by the original value and move the decimal two places right. For a quick mental estimate: if something went from $40 to $50, the difference is $10. $10 / $40 = 0.25. Move the decimal: 25% increase. For rough estimates, round the original to the nearest easy divisor — dividing by 40 in your head is easier if you think of it as "25 cents per dollar" then scale up.

What if the original value is zero — can I still calculate percentage change? No. You cannot calculate percentage change when the original value is zero because division by zero is mathematically undefined. This is a genuine limitation of the formula, not a calculator error. In contexts where a starting value of zero is possible (new product with no prior sales, for example), percentage change is not an applicable metric. Report the absolute change instead.

What is the difference between percentage change and absolute change? Absolute change is the raw difference between two values: New − Original. Percentage change expresses that difference as a proportion of the original. A stock that goes from $2.15 to $3.40 has an absolute change of $1.25 and a percentage change of 58.1%. Both numbers are accurate but tell different stories. Absolute change is more useful when comparing dollar amounts; percentage change is more useful when comparing across different scales or time periods.

If a price drops 30%, by how much does it need to increase to get back to the original? A 30% decrease requires approximately a 42.9% increase to return to the original. The calculation: if the original price is $100 and it drops 30% to $70, the increase needed is (100 − 70) / 70 × 100 = 30 / 70 × 100 = 42.9%. The required recovery percentage is always larger than the decline percentage because the recovery is calculated from a lower base.

When should I use the percentage calculator vs doing the math manually? Use the percentage calculator when accuracy matters — payroll calculations, invoice discounts, tax amounts — where a mental arithmetic error has financial consequences. Calculate by hand for quick sanity checks or when you need to show your work. The calculator is also useful when you need multiple percentage calculations in sequence (original price → sale price → tax → tip), because each step feeds into the next and manual chaining multiplies the chance of error.

Use the Free Percentage Calculator

The Free Percentage Calculator at RoughTools handles all three core percentage questions — percentage change, percentage of a number, and percentage difference — in a single tool. Enter any two known values, select what you want to find, and get an instant result with the full calculation shown. It covers percent increase, percent decrease, and side-by-side comparisons. No account needed, no data stored, completely free.

Free Percentage Calculator →

You might also need:

Discount Calculator — calculate sale prices, multi-step discounts, and final prices after percentage reductions
Percent Error Calculator — find the percentage difference between a measured value and the true value
Ratio Calculator — simplify ratios and convert between fractions, decimals, and percentages
Tip Calculator — calculate tip amounts as a percentage of a restaurant or service bill