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The core formula for any percentage change is simple:
% Change = ((New Value − Old Value) ÷ Old Value) × 100
A positive result means an increase. A negative result means a decrease. For example, going from 50 to 75 gives ((75 − 50) ÷ 50) × 100 = 50% increase.
To find a new value after a known percentage: New = Old × (1 + % ÷ 100)
To reverse a percentage and find the original: Original = New ÷ (1 + % ÷ 100)
| Situation | Old Value | New Value | Change |
|---|---|---|---|
| Salary raise | $50,000 | $55,000 | +10% |
| Price discount | $120 | $96 | −20% |
| Product markup | $40 | $60 | +50% |
| Weight loss | 90 kg | 81 kg | −10% |
| Tax added | $200 | $220 | +10% |
| Stock gain | $1,000 | $1,350 | +35% |
| Field | Typical Term | Formula Used |
|---|---|---|
| Retail | Markup / Discount | % Change |
| Finance | Return on investment | % Change |
| Payroll | Salary raise | New Value |
| Tax | Pre-tax / post-tax | Original Value |
| Science | Percent error | % Change |
| Health | BMI / weight change | % Change |
| Economics | Inflation rate | % Change |
Quick reference: what % change results from different starting values to common ending values.
| Old Value | $+10% | $+25% | $+50% | $+100% | $−10% | $−25% |
|---|
Formula: New = Old × (1 + % ÷ 100). Currency symbol ($) auto-detected from your locale. Green = increase, red = decrease.
New price at common markup and discount rates across typical price points.
| Original Price | $+5% | $+10% | $+15% | $+20% | $+50% | $−10% | $−20% | $−50% |
|---|
Price × multiplier. Example: $100 × 1.15 = $115 (15% markup). Discount: $100 × 0.80 = $80 (20% off).
Annual salary before and after common raise percentages. Useful for salary negotiations.
| Current Salary | $+2% | $+3% | $+5% | $+7% | $+10% | $+15% | $+20% |
|---|
Formula: New Salary = Current × (1 + raise% ÷ 100). All values in $ — rounded to the nearest whole number.
What multiplier (factor) matches each percentage increase or decrease. Useful for finance and investment math.
| Percent Change | Multiplier | $1,000 → | $5,000 → | $10,000 → | $50,000 → | Direction |
|---|
Multiplier = 1 + (% ÷ 100). Columns show results for common starting values in $. Negative % = multiplier below 1.
Given the final value, find what the original was before a percent increase was applied.
| Final Value | Before +5% | Before +10% | Before +15% | Before +20% | Before +25% | Before +50% |
|---|---|---|---|---|---|---|
| ($ prefixed) | Original value before the increase — shown in your local currency symbol | |||||
Formula: Original = Final ÷ (1 + % ÷ 100). Useful for finding pre-tax or pre-markup prices.
Common percentage relationships and shortcuts that are good to know.
| Rule / Fact | What It Means | Example |
|---|---|---|
| +100% | Value doubles | 50 → 100 |
| +200% | Value triples | 50 → 150 |
| −50% | Value halves | 100 → 50 |
| −100% | Value becomes 0 | 80 → 0 |
| +50% then −50% | Net result: −25% | 100 → 150 → 75 |
| +25% then −20% | Net result: 0% | 100 → 125 → 100 |
| x% of A = A% of x | Commutative property | 20% of 50 = 50% of 20 = 10 |
| 1% rule | Divide by 100 | 1% of 380 = 3.80 |
| 10% rule | Divide by 10 | 10% of 450 = 45 |
| Double then halve | Always returns to start | +100% then −50% = 0% net |
| Compound 10% × 3 yrs | ≠ 30% total | 100 → 133.1 (33.1% total) |
| Consecutive discounts | Not additive | −20% then −10% ≠ −30% |
Consecutive percentages multiply, they do not add. Always apply each step to the current value, not the original.