What is the percent-change formula?

Percent change = (new − old) ÷ old × 100%. Swapping old and new flips the sign and generally changes the magnitude because the denominator changes.

Why do I see Infinity, NaN, or an error when the old value is zero?

Relative change divides by the baseline. A true zero start makes that division undefined. Use absolute difference or choose a different reference if one applies.

How do percentage points differ from percent change?

Percentage points measure arithmetic difference between two rates (2% to 3% is +1 point). Percent change measures relative movement versus the old rate (+50% in that example). Say which one you mean.

Can I chain several percent changes?

Yes, but multiply successive factors: a +10% then −10% move uses ×1.10 × 0.90. Adding the percents as if they were independent points misstates the path.

What happens with negative old values?

The algebra still runs, yet business storytelling gets subtle (losses shrinking can look like odd positive percentages). Annotate signs carefully and consider absolute or contribution metrics when negatives dominate.

Is percent change the same as percent difference?

People use “percent difference” inconsistently—sometimes relative to the average of two values, sometimes as a synonym for percent change. This tool follows (new − old) relative to old unless the UI labels another definition.

When should I report absolute change instead?

When baselines are near zero, when units are already percentages and points are clearer, or when stakeholders need raw deltas (for example headcount +3 people).

How do I apply an increase or decrease in one step?

New = old × (1 + p/100) for an increase of p%, or old × (1 − p/100) for a decrease. That is the forward companion to measuring change between two known values.

Why isn’t a +50% followed by −50% a round trip?

Because each step uses a new base. 100 × 1.50 = 150; 150 × 0.50 = 75. Symmetric percents are not symmetric dollars.

Can I use this for temperature or other interval scales?

You can compute a relative number, but Celsius or Fahrenheit zeros are arbitrary, so percent change of temperature is often scientifically meaningless. Prefer absolute degree differences unless using an absolute scale like kelvin with care.

How should I annualize a short-period change?

Annualizing can exaggerate noisy short windows. If you do it, state the original period and method clearly, and avoid presenting extrapolated returns as guarantees.

Is input data stored?

No. Percent-change math runs in your browser for this tool.

Percent Change Calculator

Percent change answers “how much did this move relative to where it started?”—the language of price moves, traffic metrics, salaries, and inventory levels. This calculator finds the relative change from an old value to a new value, and can also apply a chosen percent increase or decrease in one step. Positive results mean growth from the baseline; negative results mean decline. Because the math always divides by the starting value, a zero baseline is undefined, and percentage points are a different concept from relative percent. Use the tool for transparent arithmetic on the numbers you supply.

Percent Change

Old valueNew value

0.00%

Apply Percentage

Base valuePercent (%)

Increased by %

Decreased by %

Informational only; verify critical results independently.

How to use

Enter the starting (old) value and the ending (new) value when you want relative change between two measurements.
Or enter one value plus a percent increase or decrease when you need to project a new figure from a known base.
Read the signed percent: positive for growth, negative for decline, relative to the old value.
Keep units comparable—same currency, same KPI definition, same period length—so the relative story is honest.
Watch the baseline carefully: the same absolute jump looks larger as a percent when the old value is small.
Distinguish percentage points from relative percent when your numbers are already rates (for example interest or unemployment).
If the old value is zero, stop and report absolute change instead; relative percent change is undefined.
For multi-step moves, apply each percent on the current base or multiply growth factors rather than adding percentages.
Round for your audience: finance decks may show one decimal place while science contexts keep more.
Label the time window clearly when you later annualize or compare to other series so readers are not misled.

Examples

Stock $40 → $46: (46 − 40) ÷ 40 × 100 = +15% gain.
Users 10,000 → 12,500: (12,500 − 10,000) ÷ 10,000 × 100 = +25% growth.
Apply 8% decrease to $89.99: 89.99 × 0.92 ≈ $82.79.
Salary $75,000 → $82,000: (82,000 − 75,000) ÷ 75,000 × 100 ≈ +9.33%.
Price $50 → $40: (40 − 50) ÷ 50 × 100 = −20% change.
Apply 6% increase to 250: 250 × 1.06 = 265.
Metric 200 → 200: percent change = 0%.
Recovery trap: 100 → 80 is −20%; 80 → 100 is +25% from the new base—not a mirror image.
Rate story: 2% → 3% is +1 percentage point but +50% relative to the old rate of 2%.
Error case: old value 0 and new value 10 → percent change undefined; report +10 absolute units instead.

FAQ

What is the percent-change formula?: Percent change = (new − old) ÷ old × 100%. Swapping old and new flips the sign and generally changes the magnitude because the denominator changes.
Why do I see Infinity, NaN, or an error when the old value is zero?: Relative change divides by the baseline. A true zero start makes that division undefined. Use absolute difference or choose a different reference if one applies.
How do percentage points differ from percent change?: Percentage points measure arithmetic difference between two rates (2% to 3% is +1 point). Percent change measures relative movement versus the old rate (+50% in that example). Say which one you mean.
Can I chain several percent changes?: Yes, but multiply successive factors: a +10% then −10% move uses ×1.10 × 0.90. Adding the percents as if they were independent points misstates the path.
What happens with negative old values?: The algebra still runs, yet business storytelling gets subtle (losses shrinking can look like odd positive percentages). Annotate signs carefully and consider absolute or contribution metrics when negatives dominate.
Is percent change the same as percent difference?: People use “percent difference” inconsistently—sometimes relative to the average of two values, sometimes as a synonym for percent change. This tool follows (new − old) relative to old unless the UI labels another definition.
When should I report absolute change instead?: When baselines are near zero, when units are already percentages and points are clearer, or when stakeholders need raw deltas (for example headcount +3 people).
How do I apply an increase or decrease in one step?: New = old × (1 + p/100) for an increase of p%, or old × (1 − p/100) for a decrease. That is the forward companion to measuring change between two known values.
Why isn’t a +50% followed by −50% a round trip?: Because each step uses a new base. 100 × 1.50 = 150; 150 × 0.50 = 75. Symmetric percents are not symmetric dollars.
Can I use this for temperature or other interval scales?: You can compute a relative number, but Celsius or Fahrenheit zeros are arbitrary, so percent change of temperature is often scientifically meaningless. Prefer absolute degree differences unless using an absolute scale like kelvin with care.
How should I annualize a short-period change?: Annualizing can exaggerate noisy short windows. If you do it, state the original period and method clearly, and avoid presenting extrapolated returns as guarantees.
Is input data stored?: No. Percent-change math runs in your browser for this tool.

Formula / Method

Percent change = ((new − old) ÷ old) × 100. Apply +p%: new = old × (1 + p/100). Apply −p%: new = old × (1 − p/100). Absolute change = new − old (use when old = 0 or when relative framing misleads).

Assumptions & Limitations

Requires a non-zero old value for relative change. Does not choose among competing “percent difference” definitions or apply compounding calendars beyond the steps you enter. Negative bases need careful interpretation. This is an arithmetic helper only—not investment, tax, or statistical advice.

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Last updated: 2026-07-13

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