How to Calculate Percentage Change: The Formula

Percentage change tells you how much a value has risen or fallen relative to where it started. The formula is: ((New Value − Old Value) ÷ Old Value) × 100. A positive result means an increase; a negative result means a decrease. That's the complete answer — everything else on this page is context and worked examples.

For example, if a product cost £50 last month and costs £60 today, the percentage change is ((60 − 50) ÷ 50) × 100 = +20%. You can use this formula with any two numbers — prices, weights, scores, population figures, or investment values.

How to Calculate a Percentage Increase

Say a salary rises from £40,000 to £52,000. Plug the numbers into the formula:

  1. Subtract the old value from the new value: 52,000 − 40,000 = 12,000
  2. Divide by the old value: 12,000 ÷ 40,000 = 0.3
  3. Multiply by 100: 0.3 × 100 = 30%
The salary increased by 30%. Notice that you always divide by the starting value, not the new one. A common mistake is dividing by the new value, which gives a different — and wrong — answer. The old value is your baseline reference point.

How to Calculate a Percentage Decrease

The same formula handles decreases automatically. Suppose someone's weight drops from 90 kg to 81 kg:

  1. New minus old: 81 − 90 = −9
  2. Divide by old: −9 ÷ 90 = −0.1
  3. Multiply by 100: −0.1 × 100 = −10%
The negative sign confirms it's a decrease. So the person lost 10% of their starting body weight. You don't need a separate formula for decreases — the sign takes care of itself. If you want to express it as a plain decrease, just drop the minus and say "a 10% reduction."

Percentage Change vs Percentage Points: A Critical Distinction

These two terms are frequently confused, and mixing them up leads to seriously misleading statements. Percentage change is a relative measure — it compares the change to the original value. Percentage points is an absolute measure — it's simply the arithmetic difference between two percentages.

Example: if a tax rate rises from 20% to 25%, that is a 5 percentage point increase, but a 25% percentage change ((25−20)÷20×100 = 25%). Politicians and journalists often say "X% increase" when they mean "X percentage points" — always check which one is being used before drawing conclusions.

Common Mistakes When Calculating Percentage Change

Even people comfortable with maths make these errors regularly:

  • Dividing by the wrong value — always divide by the original (old) value, not the new one
  • Reversing the subtraction — it must be new minus old, not old minus new
  • Confusing percentage change with percentage points — see the section above
  • Applying percentage change symmetrically — a 50% increase followed by a 50% decrease does NOT return you to the starting point (you end up at 75% of the original)
  • Using the wrong base for comparisons — if comparing two periods, be consistent about which period is "old"

When to Use a Calculator vs Doing It Manually

For quick mental estimates, there are handy shortcuts: a 10% change is just moving the decimal point; a 5% change is half of that. For rough comparisons in conversation, mental arithmetic is usually fine. However, for anything that matters — finance, health metrics, business reporting — use a dedicated tool. Manual calculations introduce rounding errors and transcription mistakes, especially across multiple figures. The free percentage calculator at allio.tools handles percentage change, percentage of a value, and reverse percentage in one place, with no sign-up required.

3 Real-World Uses of Percentage Change

Percentage change appears constantly in everyday life:

  • Salary raises — if you earn £35,000 and are offered a £2,100 raise, that's (2,100 ÷ 35,000) × 100 = 6% — a useful figure to benchmark against inflation
  • Price changes — retailers mark items "Was £80, Now £56" — the percentage change is ((56−80)÷80)×100 = −30%, meaning a 30% discount
  • Investment returns — if a portfolio moves from £10,000 to £13,400 over a year, the return is ((13,400−10,000)÷10,000)×100 = 34% — far more meaningful than just the £3,400 gain in isolation