How do I find X% of a number?+
Divide X by 100 to convert to a decimal, then multiply by the number. Example: 35% of 240 = (35/100) × 240 = 0.35 × 240 = 84. Mental shortcut: 10% of any number is just moving the decimal one place left; then scale (30% = 3× that, 5% = half of 10%, etc.).
How do I calculate percentage change between two numbers?+
Formula: ((New − Old) / Old) × 100. Example: price was $50, now $65: change = ((65−50)/50)×100 = (15/50)×100 = 30% increase. For a decrease: price was $80, now $60: ((60−80)/80)×100 = (−20/80)×100 = −25% change. The old value is always the denominator.
How do I reverse a percentage increase to find the original value?+
Divide the current value by (1 + rate/100). After a 25% increase resulting in $125: original = 125/1.25 = $100. After a 15% decrease resulting in $85: original = 85/0.85 = $100. Common error: subtracting the same percentage from the new value (125−25%=93.75 is wrong because 25% of 125 ≠ 25% of 100).
What is the difference between margin and markup?+
Both express profit as a percentage but use different bases. Markup = (Profit / Cost) × 100 — often used by manufacturers and retailers when pricing from cost. Margin = (Profit / Selling Price) × 100 — used in financial reporting and accounting. To convert: margin = markup / (100 + markup) × 100. A 50% markup = 33.3% margin.
How do I calculate a tip and split a bill?+
Tip amount = Bill × (tip% / 100). Total per person = (Bill + Tip) / Number of people. Example: $120 bill, 18% tip, 4 people: Tip = $120 × 0.18 = $21.60. Total = $141.60. Per person = $141.60 / 4 = $35.40. Some prefer applying tax before tip (tip on total), others on pre-tax — convention varies by region.
What is compound growth and how does it differ from simple percentage?+
Simple: interest calculated on principal only. A = P × (1 + r×t). Compound: interest earns interest too. A = P × (1 + r/n)^(n×t). Example: $1,000 at 10% for 5 years. Simple: $1,000+$500=$1,500. Compound annually: $1,000×1.1^5=$1,610.51. The more compounding periods, the higher the result. Rule of 72: years to double ≈ 72/rate%.
How do I calculate a percentage of a percentage?+
Multiply the two percentages together. "30% of 40%" = 0.30 × 0.40 = 0.12 = 12%. Used in probability: P(A and B) = P(A) × P(B) for independent events. Also used in cascaded discounts: 20% off, then extra 10% off = 1×0.80×0.90 = 0.72 = 28% total off, not 30% off.
What is percentage completion and how is it calculated?+
Percent complete = (Work Done / Total Work) × 100. Used in project management, manufacturing, and construction. Example: 150 of 400 units assembled = (150/400)×100 = 37.5% complete. Variations: cost-based completion uses cost incurred vs. budget; units-based uses items finished vs. total items planned.
How does VAT or sales tax percentage work?+
Tax amount = Price × (tax% / 100). Price with tax = Price × (1 + tax%/100). To find pre-tax price from tax-inclusive amount: Pre-tax = Inclusive / (1 + tax%/100). Example: $108 inclusive of 8% tax: Pre-tax = $108/1.08 = $100. Tax = $8. In EU VAT contexts, inclusive pricing is standard; in US, taxes are added at checkout.
How do percentages work in statistics and probability?+
In statistics, percentages express frequencies (60% of respondents), relative probabilities (30% chance), percentile ranks (90th percentile = better than 90% of values), and composition (portfolio allocation 40%/35%/25%). Probability: convert % to decimal (35% = 0.35). Percentile rank ≠ percentage score: a 75th percentile student scored better than 75% of others, but their raw score could be 60%.
What does "basis points" mean in finance?+
A basis point (bp) = 1/100 of a percentage point = 0.01%. So 100 basis points = 1%. Used for interest rates, bond yields, and spreads because small changes matter: "The Fed raised rates 25bps" = 0.25% increase. Finance uses basis points to avoid ambiguity between percentage points and percent change: "rates rose 50bps from 4.00% to 4.50%" is unambiguous.
How do I check if my percentage calculation is correct?+
Quick verification: the part should always be proportionally reasonable to the whole. If 30% of 200 = 60, check: 10%=20, 30%=60 ✓. For percentage change: re-apply the change to the original to verify. For reverse percentage: apply the percentage to your answer to get back the result. Many errors come from wrong base (new vs old, cost vs price) — always confirm which is 100%.