Percentage Increase Calculator
Change with direction: the growth from A to B in percent, the multiplier that did it, and the stacked-change laws intuition gets wrong.
Percentage Increase Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- One change at a time — chains are doctrine, not fields.
- Positive quantities only.
- No compounding-period model (finance owns growth rates).
In short: 80 up to 100: (100 − 80) ÷ 80 × 100 = +25% — a ×1.25 multiplier, undone by dividing by 1.25. Stack +10% then +20% on 100 and you reach 132 — +32%, not 30%, because the second percent rides the bigger base. And +50% followed by −50% lands on 75, not 100.
Formula
increase % = (B − A) ÷ A × 100
multiplier = B ÷ A = 1 + rate
stacked: ×1.10 × 1.20 = ×1.32 = +32%
reverse: A = B ÷ multiplier
[('original', 'the denominator is where you STARTED'), ('×1.32', '+10% then +20% — stacked multiplies'), ('75', '+50% then −50% — never cancels'), ('22.2%', '40 vs 50 with no direction: percent difference')]
Worked Example
- Name the original and the new value — direction matters.
- (B − A) ÷ A × 100.
- Read the multiplier for stacking and undoing.
- Stack by multiplying factors, never by adding percents.
- No direction? Percent difference over the average.
80 → 100 = +25%, multiplier ×1.25, undo = ÷1.25. Stacked +10/+20 = +32%. +50/−50 lands on 75. Percent difference 40 vs 50 = 22.2%.
Strengths & Limits Of This Model
Where this engine is strong
- Multiplier and undo as first-class outputs
- The +32% stacked truth stated as arithmetic
- Percent-difference fork honestly separated
Where it stops
- No period fields
- No log-return framing
Practical Use Cases
Raises
Salary growth, then its honest undo.
Price histories
Growth priced from the original.
Population data
The 20,000 → 21,250 pattern.
Stacked raises
Why +10 then +20 is +32.
Sales-year comparisons
Multipliers beat memory.
Methodology & Editorial Standards
pct = (B − A) ÷ A × 100 with A the original; multiplier = B ÷ A; reversing stated as division by the multiplier. The note derives the stacked-factor law (×1.10 × 1.20 = ×1.32) and the round-trip asymmetry (×1.5 × 0.5 = 0.75), plus the percent-difference card (|B−A| over the mean) for directionless pairs. Non-positive originals or new values refused.
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Percentage Increase Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
How do I calculate percentage increase?
(New − Original) ÷ Original × 100. From 80 to 100: the 20-step divided by the original 80 is +25%. The value you started with is always the denominator.
Why is a 25% rise not undone by a 25% fall?
Because the second percent rides a different base. 80 × 1.25 = 100, but 100 × 0.75 = 75. To reverse a ×1.25 exactly, divide by 1.25: 100 ÷ 1.25 = 80.
Is +10% then +20% a 30% increase?
No — 100 × 1.10 = 110, then ×1.20 = 132. That is +32%. Stacked changes multiply their factors; adding percents double-counts the base.
What is the difference between percent change and percent difference?
Change has a direction: 40 to 50 is +25% over the original. Difference does not: two independent values compare over their AVERAGE, so 40 vs 50 is 10 ÷ 45 = 22.2%. Choosing the wrong denominator is the whole mistake.
What if the new value is smaller?
The formula returns a negative percent — that is a decrease, and the Decrease page frames it with its own doctrine (points, stacked discounts).
Why can't the original be zero?
Percent change is division by the original. From zero, every positive value is an infinite percent up — the question has no honest answer, so the page refuses.
How do I add a percentage to a number?
Multiply by 1 plus the rate: adding 25% is ×1.25, so 80 × 1.25 = 100. The multiplier IS the increase in operational form — which is why stacking and undoing are single multiplications on this page.
Where is percentage POINTS on this page?
They are not — points compare two percentages (10% to 12%), not two quantities. The Decrease page owns that distinction with a live calculator for it.