Percentage Increase and Decrease Guide
Formulas for percent change, increase, decrease, and the common mistake of using the wrong base value — with worked examples.
7 min read · Last updated: July 13, 2026
Percent change between two values
Percent change = ((new value − old value) ÷ old value) × 100. The old (starting) value is always the denominator — this is the most common error in percent-change math. Example: a price rises from $80 to $100. Change = ((100 − 80) ÷ 80) × 100 = 25% increase. Dropping from $100 to $80 is ((80 − 100) ÷ 100) × 100 = −20% — not symmetric, because the bases differ. Headlines often report the larger number as the base to exaggerate a recovery or decline; always check which value sits in the denominator before trusting a percentage claim.
Increase or decrease by a percent
New value = original × (1 + p/100) for an increase, or original × (1 − p/100) for a decrease, where p is the percentage. A 15% raise on $50,000 salary: 50,000 × 1.15 = $57,500. A 30% sale on a $120 item: 120 × 0.70 = $84. Chaining changes multiplies factors: +10% then −10% gives 1.10 × 0.90 = 0.99 — a net 1% loss, not zero. Three years of 5% annual raises on $50,000: 50,000 × (1.05)³ ≈ $57,881, not 50,000 × 1.15. Use exponents when the same percent repeats over multiple periods.
Finding the original before a percent was applied
If you know the result after a percent change, divide by the multiplier. After a 25% markup, a shelf price of $125 means cost = 125 ÷ 1.25 = $100. After a 20% discount, a sale price of $64 means original = 64 ÷ 0.80 = $80. This reverse calculation is essential for margin and discount analysis in retail and finance. Stacked discounts do not add: 20% off then an extra 10% off is 0.80 × 0.90 = 0.72 of the original — 28% total off, not 30%. Apply each step sequentially or multiply the remaining fractions.
Markup vs margin — different bases
Markup percent = (selling price − cost) ÷ cost × 100. Margin percent = (selling price − cost) ÷ selling price × 100. A $100 cost sold at $150 is 50% markup but only 33.3% margin — same dollars, different denominators. Confusing the two leads to underpricing. Always identify whether the percentage is applied to cost (markup) or revenue (margin). To hit a 40% margin, price = cost ÷ (1 − 0.40). For $100 cost, that is 100 ÷ 0.60 ≈ $166.67 — not $140 (which would be 40% markup). Retail and SaaS pricing both depend on getting this base right.
Quick reference examples
Tip: 18% of a $85 bill = 0.18 × 85 = $15.30. Tax: 8.25% on $200 = 0.0825 × 200 = $16.50. Population growth: town grows from 12,000 to 13,800 → ((13,800 − 12,000) ÷ 12,000) × 100 = 15%. Stock drop: $48 to $36 → ((36 − 48) ÷ 48) × 100 = −25%. Each case uses the same core formulas with different labels. Percentage points differ from percent change: unemployment falling from 8% to 6% is a 2 percentage-point drop but a 25% relative decrease ((6−8)/8). Precision in language prevents misread reports.
Common mistakes to avoid
Using the new value as the denominator when calculating change. Adding percentages that apply to different bases (e.g., 10% tax on a discounted price). Assuming symmetric up/down moves cancel out. Treating markup and margin as interchangeable. Forgetting that 'percent off' applies to the current price, not always the original list price. When in doubt, write the formula with concrete numbers — if $80 → $100 is +25%, verify by checking 80 × 1.25 = 100 before publishing or presenting the figure.
Calculate on CalcVo
The CalcVo Percentage Calculator handles percent-of, change, increase, decrease, and reverse modes. Use the Discount Calculator for sale prices, the Tip Calculator for restaurant splits, and the Markup or Margin Calculators when pricing products. The Profit Margin Calculator ties revenue, cost, and margin together. Every result updates live as you edit inputs — useful for checking homework, invoices, or pricing spreadsheets.