Percentage Decrease Calculator
Reduction done honestly: the drop from A to B, the percentage-points card that separates 2 points from 20 percent, and why stacked discounts never add.
Percentage Decrease Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- One reduction per calculation.
- Points card assumes positive rates.
- No compounding depreciation schedule.
In short: 100 down to 80: (100 − 80) ÷ 100 × 100 = 20% down — a ×0.80 multiplier, undone by ÷0.80. A rate moving 10% to 12% rose 2 percentage POINTS but 20 PERCENT. A 20%-off sign followed by 10% off is 28% total (×0.8 × 0.9 = 0.72), never 30%.
Formula
decrease % = (A − B) ÷ A × 100
multiplier = B ÷ A = 1 − rate
points = p2 − p1; percent = (p2 − p1) ÷ p1 × 100
stacked discounts: ×0.8 × 0.9 = ×0.72 = 28% off
[('original', 'the denominator, always the starting value'), ('2 pts ≠ 20%', 'points subtract; percent divides'), ('×0.72', '20% then 10% off — 28%, never 30%'), ('÷0.80', 'restoring is division by the factor')]
Worked Example
- Name the original and the reduced value.
- (A − B) ÷ A × 100 — the drop in percent.
- Use the second pair for the points-vs-percent read.
- Stack discounts by multiplying the survivors.
- Undo any cut by dividing by its factor.
100 → 80 = 20% down, ×0.80, undo = ÷0.80. 10% → 12% = +2 pts = +20%. 20%-off then 10%-off = 28% total.
Strengths & Limits Of This Model
Where this engine is strong
- Points AND percent printed together, signed
- Stacked discounts killed by arithmetic, not opinion
- Restoration-as-division stated twice
Where it stops
- No schedule fields
- No currency rounding model
Practical Use Cases
Sale signs
The stacked-discount truth.
Rates & bands
Points versus percent, live.
Weight loss
Reduction against the start.
Price drops
The multiplier and the undo.
Depreciation
First-year honesty.
Methodology & Editorial Standards
pct = (A − B) ÷ A × 100 with A the original; multiplier = B ÷ A; restoration stated as division. The points card takes a second pair of rates and prints BOTH units: p2 − p1 in points and (p2 − p1) ÷ p1 × 100 in percent. The stacked-discount law (×0.8 × 0.9 = ×0.72) is derived in the note. Non-positive originals refused; negative reduced values refused as non-discounts.
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 Decrease 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 decrease?
(Original − New) ÷ Original × 100. From 100 to 80: the 20-step over the original 100 is 20%. The starting value is always the denominator.
What is the difference between percentage points and percent?
Points subtract; percent divides. A rate from 10% to 12% moved +2 percentage points but rose (12 − 10) ÷ 10 = +20% relative. A 2-point move on a small base is a big percent.
Is 20% off then 10% off the same as 30% off?
No — ×0.80 × 0.90 = ×0.72, which is 28% off. The second discount applies to the already-reduced price, so stacking always disappoints addition.
How do I reverse a 20% discount?
Divide by the survival factor. 80 ÷ 0.80 = 100. Adding 20% back gives 96 — a different number entirely, because the percent re-rides a smaller base.
Why is a drop from 100 to 80 only 20% while a rise from 80 to 100 is 25%?
Both moves are 20 units, but percent prices them against where you started: 20/100 then 20/80. Direction changes the denominator, so the percents never mirror.
Can the reduced value go below zero?
Not as a discount — this page takes zero or more. Negative results are debts or losses, different tools entirely.
How do I take 20% off a price?
Multiply by the survivor: 100 − 20% is ×0.80, so the price pays 80% of itself. For stacked sales keep multiplying survivors — 20% then 10% off is ×0.80 × 0.90 = ×0.72, 28% total.
What if my two rates moved the other way?
The points card shows the sign: 12% back to 10% is −2 points and −16.7% relative — both readings on one card.