Calculate percentage improvement, apply a percent change to find a new value, or reverse-calculate the original from a changed value.
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Improvement Percentage Formula
The calculator runs three modes. Each uses one of the formulas below.
1. Percentage change (find the improvement %):
Improvement % = ((New − Original) / |Original|) × 100
2. Apply a percentage (find the new value):
New = Original × (1 + % / 100)
3. Reverse calculation (find the original value):
Original = New / (1 + % / 100)
- Original — the starting or baseline value.
- New — the value after the change.
- % — the improvement, expressed as a percentage.
Notes: The denominator uses the absolute value of the original so a negative baseline still gives a sensibly signed result. A positive % means improvement (increase), a negative % means decline. The original value cannot be zero in mode 1, and the percentage cannot be −100% in mode 3, since both cause division by zero.
Reference Values
Use these to sanity-check a result before reporting it.
| Improvement % | Multiplier | Interpretation |
|---|---|---|
| 0% to 5% | 1.00 – 1.05 | Slight, often within noise |
| 5% to 20% | 1.05 – 1.20 | Moderate improvement |
| 20% to 50% | 1.20 – 1.50 | Strong improvement |
| 50% to 100% | 1.50 – 2.00 | Large; verify inputs |
| > 100% | > 2.00 | More than doubled |
| Original | New | Improvement |
|---|---|---|
| 100 | 110 | +10% |
| 100 | 125 | +25% |
| 80 | 100 | +25% |
| 200 | 150 | −25% |
| 50 | 75 | +50% |
Example Problems
Test score went from 72 to 90.
((90 − 72) / 72) × 100 = (18 / 72) × 100 = 25% improvement.
Run time dropped from 30 minutes to 24 minutes.
((24 − 30) / 30) × 100 = −20%. For a metric where lower is better, that −20% is the improvement. Always state the direction so the sign is not misread.
Sales were $4,000 and grew 18%. New sales?
4000 × (1 + 0.18) = $4,720.
FAQ — Why use |Original| in the denominator? If the baseline is negative, dividing by the raw value flips the sign of the result and mislabels gains as losses. Using the absolute value preserves direction.
FAQ — Improvement vs. percentage point? A jump from 40% to 50% is a 10 percentage point change but a 25% improvement. The calculator returns the relative percentage, not percentage points.
