Percentage change formula (the exact math)

Percentage change answers a simple question: “How big is the change compared to where I started?” That “where I started” piece is the key. We always measure the change relative to the old value.

• Absolute change: Δ = New − Old
• Percent change: % Change = (Δ ÷ Old) × 100

• If % Change is positive, it’s a percent increase.
• If % Change is negative, it’s a percent decrease.
• If % Change is 0, there is no change.

• If Old = 0 and New = 0, the change is 0 (nothing changed).
• If Old = 0 and New ≠ 0, percent change is not defined (division by zero).
• In real life, you can describe it as “went from zero to New” or “infinite growth”, but mathematically it’s undefined.

That’s why this calculator gives you a clear message when Old is zero. It’s not being picky — it’s avoiding a misleading number.

Percent change depends heavily on the baseline. A $20 increase on an $80 item is a 25% increase, but the same $20 increase on a $400 item is only 5%. This is why percent change is great for comparing growth rates, but you should often pair it with the absolute change so you don’t lose the real-world scale.

Real-world percentage change examples

Below are a few quick examples you can copy/paste into the calculator. Notice how the same absolute change can produce a different percent change depending on the baseline (old value).

• Old = 80, New = 100 → Δ = 20
• % Change = (20 ÷ 80) × 100 = 25% increase

• Old = 120, New = 90 → Δ = −30
• % Change = (−30 ÷ 120) × 100 = −25% (25% decrease)

• Old = 2,000 visits, New = 2,800 visits → Δ = 800
• % Change = (800 ÷ 2,000) × 100 = 40% increase

You can still compute percent change when the old value is negative, but interpretation depends on context (for example: losses vs profits). The formula stays the same.

• Old = −50, New = −20 → Δ = 30
• % Change = (30 ÷ −50) × 100 = −60%

If that looks strange, it’s because the baseline is negative. In analytics and finance, always pair the percent result with a plain-English explanation of what the signs mean.

What this calculator does step-by-step

Even though the result feels instant, there are a few steps happening behind the scenes. Understanding them helps you sanity-check results and avoid common spreadsheet mistakes.

The calculator accepts decimals and negative numbers. It also supports formats like “1,234.56” by safely removing commas and spaces before converting to a number.

Absolute change is simply New − Old. It tells you the raw movement in the same units as your original values (dollars, pounds, points, clicks, etc.).

Percent change is (Absolute change ÷ Old) × 100. This converts your change into a percent of your baseline. The calculator then labels it as an increase, decrease, or no change.

If Old is 0, percent change is undefined (division by zero). Instead of showing a misleading number, the calculator explains the situation clearly.

Tap Save Result to keep up to 10 recent results on this device. Use the share buttons to send a clean summary to WhatsApp, Telegram, Twitter/X, Facebook, or LinkedIn.

Frequently Asked Questions

• What is percentage change?

  Percentage change measures how much a value increased or decreased relative to the starting (old) value. It’s calculated as (New − Old) ÷ Old × 100.

• How do I calculate percent increase?

  If New > Old, the percent change is positive and represents a percent increase. Use the same formula; the sign tells you the direction.

• How do I calculate percent decrease?

  If New < Old, the percent change is negative. The magnitude (absolute value) is the “percent decrease.”

• Why is percent change undefined when Old = 0?

  Because the formula divides by Old. Division by zero isn’t defined in standard arithmetic. If you go from 0 to 10, you can describe it in words, but a percent is not mathematically valid.

• Can percent change be over 100%?

  Yes. If New is more than double Old, the change is above 100%. Example: 50 → 200 is a 300% increase.

• Is percent change the same as percent difference?

  No. Percent change uses Old as the baseline (before → after). Percent difference treats both values symmetrically (often using an average baseline).

Make it viral (without being spammy)

The most shareable results are the surprising ones: “My rent jumped 18.2%” or “My page views grew 142%.” If you’re posting the result, include Old and New so people can learn and trust the math.

• Money: “Old → New = X% change”
• Analytics: “We grew by X%”
• School: “Score improved by X%”
• Fitness: “Weight changed by X%”