Perform percentage calculations easily and quickly. Calculate A's B%, compare what percent A is of B, calculate increase/decrease rates, and find values after percentage changes in real-time.
A percentage (%) is a ratio based on 100. "Percent" comes from Latin "per centum" meaning "per hundred". For example, 50% means 50 out of 100, or half. Percentages are widely used: discounts (30% off), test scores (85/100 = 85%), interest rates (3% annual interest), growth rates (10% year-over-year growth). The basic formula is (part/whole) Γ 100 = percentage.
Calculating A's B% is the most basic percentage calculation. The formula is A Γ (B/100). Shopping discount: 20% off a $100 item is $20 off, final price $80. Tax: 15% income tax on $50,000 is $7,500. Tip: 10% tip on $50 meal is $5. Bank interest: 3% annual interest on $100,000 yields $3,000 after one year.
The formula for what % A is of B is (A/B) Γ 100. Test score: 85 out of 100 is 85%. 90 out of 120 is 75%. Goal achievement: $700,000 of $1,000,000 target is 70%. Market share: $5 billion revenue in a $50 billion market is 10%. Values can exceed 100%: achieving $1.5M against a $1M goal is 150%.
The formula for increase or decrease rate is ((After - Before) / Before) Γ 100. Positive results indicate increase, negative indicate decrease. Price increase: $0.80 to $0.92 is a 15% increase. Salary raise: $3,000 to $3,300 is 10%. Weight loss: 80kg to 72kg is -10%, or 10% decrease. Stock: $50,000 to $62,500 is 25% up.
Calculate the value after a percentage increase or decrease. Increase formula: Original Γ (1 + Percent/100). Decrease formula: Original Γ (1 - Percent/100). Price increase: $100 with 20% increase is $120. Discount: $50 with 30% discount is $35. Population growth and depreciation use the same multiplicative approach.
When applying percentages sequentially, apply each to the previous result. Important: 10% increase then 10% decrease does not return to the original value. $100 + 10% = $110, $110 - 10% = $99. Sequential discounts: $100 with 20% then 10% discount = $72 (total 28%, not 30%). Compound interest: $100,000 at 5% for 3 years = $115,762.50.
The discount rate is the reduction from list price; the margin rate is the share of profit in revenue. Discount: a $100 item sold at $70 is 30% off. Margin: cost $60, price $100 gives $40 profit and a 40% margin. Markup (cost-based) is 66.7%. A coffee costing $1 sold at $4 has a 75% margin and 300% markup.
Percentages are essential in tax. VAT 10%: a net $100 plus $10 VAT is a gross $110; reversing, $110 / 1.1 = $100 net. Withholding 3.3%: on $2,000 freelance income the tax is $66, net $1,934. Progressive taxes apply different rates by bracket.
Pitfall 1 (base confusion): if A is 120 and B is 100, A is 20% more than B but B is 16.7% less than A. Pitfall 2 (sequential discounts): 20% + 10% is 28% off, not 30%. Pitfall 3 (percentage points vs percent): a rate rising from 5% to 6% is +1 percentage point but a 20% increase. Always verify with a reverse calculation.