Percentage increase formula

The phrase percentage increase means: “How much did the value rise compared to where it started?” That “compared to where it started” part is the key—percent increase always uses the old value as the baseline.

First, compute the raw change: Increase = New − Old. If the result is positive, you’ve got an increase. If it’s negative, the new value is smaller and you actually have a decrease.

Next, convert the change into a fraction of the old value: (New − Old) ÷ Old. This answers: “What fraction of the original value is the change?”

Finally, multiply by 100 to express the fraction as a percentage: % Increase = ((New − Old) ÷ Old) × 100. A result of 25% means the value increased by one quarter of its original amount.

If the old value is 0, percentage increase is not defined because you can’t divide by zero. In real life, people sometimes say “it went from 0 to 10, that’s infinite %,” which is why this calculator will show a clear error and suggest alternatives.

Real-world percentage increase examples

Old price = 80, new price = 100. The increase is 100 − 80 = 20. Divide by the old value: 20 ÷ 80 = 0.25. Multiply by 100: 0.25 × 100 = 25%. So the price increased by 25%.

Old salary = 60,000 and new salary = 66,000. Increase = 6,000. Percent increase = 6,000 ÷ 60,000 × 100 = 10%. Translation: “A 10% raise.”

Old lift = 135 lb, new lift = 185 lb. Increase = 50 lb. Percent increase = 50 ÷ 135 × 100 ≈ 37.04%. That’s a big jump—nice.

Old value = 100, new value = 90. Increase = 90 − 100 = −10, percent change = −10 ÷ 100 × 100 = −10%. That means a 10% decrease. If you only care about decreases, use the Percentage Decrease tool.

What this calculator does (in plain English)

When you click Calculate, the tool:

• Validates that both numbers are provided and that the old value is not zero.
• Computes the change: New − Old.
• Divides that change by the old value to get the change fraction.
• Multiplies by 100 to convert the fraction to a percent.
• Formats the output to your chosen decimal places.
• Shows the steps so you can copy the math into homework, slides, or a spreadsheet.

The output is designed to be instantly shareable: a short “headline” result plus an optional step-by-step breakdown for people who want to verify it.

Frequently Asked Questions

• What’s the difference between percent change and percent increase?

  “Percent change” can be either positive (increase) or negative (decrease). “Percent increase” specifically focuses on rises. The math is the same; it’s the interpretation that changes.

• What if my old value is negative?

  The formula still works, but the interpretation can be tricky because the baseline is negative. In finance, you may want to think carefully about what the “starting point” means.

• Why can’t you calculate percent increase from 0?

  Because percentage increase divides by the old value. Division by zero is undefined, so the result would be mathematically meaningless (often described as “infinite”).

• How do I reverse the calculation?

  If you know the old value and the percent increase, the new value is: New = Old × (1 + percent/100). If you know the new value and want to find the old, rearrange: Old = New ÷ (1 + percent/100).

• Should I use percent difference instead?

  If neither value is clearly “the original” (for example, comparing two measurements where both are equally valid), percent difference uses an average baseline and can be more fair. Try Percent Difference.

• Can I copy/paste this into Excel or Google Sheets?

  Yes. In spreadsheets, percent increase is often: ((New - Old) / Old) and then formatted as a percentage. Or multiply by 100 if you want the numeric percent value.

Make this page shareable

Percentage increase is a “viral” concept because it instantly answers questions people argue about: “Is this actually a big raise?” “How much did the price jump?” “Did we really grow last month?” For maximum shareability, screenshot the result block and post it with the before/after numbers.

• Use it for “price went up” receipts (old vs new screenshots).
• Post a “salary raise calculator” screenshot (no personal info, just percentage).
• Use it in business updates: weekly traffic up/down with %.
• Link to related tools like CAGR and compound interest for deeper finance stories.