Percentage Calculator

Multiply Y by X, then divide by 100. Formula: Result = Y × X / 100. Example: What is 15% of 200? Calculation: 200 × 15 / 100 = 30. A mental shortcut: first find 10% (move the decimal left one place), then add half of that for 15%. 10% of 200 = 20. Half of 20 = 10. Total = 30.

Divide X by Y and multiply by 100. Formula: Percentage = (X / Y) × 100. Example: 30 is what percent of 200? Calculation: (30 / 200) × 100 = 15%. This is the reverse of Calculator 1. You can check your answer using Calculator 1: 15% of 200 = 30.

Percentage change = ((New Value − Old Value) / |Old Value|) × 100. A positive result is an increase; negative is a decrease. Examples: Price rose from $100 to $120: ((120 − 100) / 100) × 100 = +20% increase. Price fell from $200 to $150: ((150 − 200) / 200) × 100 = −25% decrease. Note: use the original (old) value as the denominator, not the new value.

Use Calculator 1 above. For a 20% tip on a $75 bill: What is 20% of 75? = 75 × 20 / 100 = $15. Mental shortcut for 20%: divide by 10 ($7.50), then double ($15). For 15% tip: find 10% ($7.50), add half ($3.75), total = $11.25. For 18% tip: find 10% ($7.50) + find 8% (find 10% and subtract 20%) = $6 + total $13.50.

Two approaches: (1) Find the discount amount and subtract. Discount amount = Original price × Discount % / 100. Sale price = Original − Discount. Example: 30% off $80 = $80 × 30 / 100 = $24 discount. Sale price = $80 − $24 = $56. (2) Multiply by the complement. Sale price = Original × (1 − Discount%/100) = $80 × 0.70 = $56. Both methods give the same answer. Calculator 1 gives you the discount amount; subtract manually for the sale price.

Formula: Final price = Original × (1 + Percentage / 100). Example: $45 item with 8% sales tax: $45 × 1.08 = $48.60. For a 7.5% tax on $120: $120 × 1.075 = $129. You can also use Calculator 1 to find the tax amount (8% of $45 = $3.60) and add it manually ($45 + $3.60 = $48.60). The multiplication method is faster for round tax rates.

This is one of the most common sources of confusion in business and media. A percentage point is an absolute difference between two percentages. A percent change is a relative difference. Example: interest rates rise from 2% to 3%. The increase is 1 percentage point (3 − 2 = 1). But the percent change is 50% ((3 − 2) / 2 × 100 = 50%). Politicians and media often use percentage points when the percent change would sound more dramatic, or vice versa. Always check which is being reported.

If you know the result of a percentage calculation but want the original, divide by the decimal form. Example: After a 20% increase, a salary is $60,000. What was the original? $60,000 / 1.20 = $50,000. Example: A shirt costs $35 after a 30% discount. Original price? $35 / 0.70 = $50. The key: 20% increase means the result is 120% of original (multiply by 1.20). 30% decrease means the result is 70% of original (multiply by 0.70). To reverse, divide by that decimal.

You cannot simply add percentage changes. A 10% increase followed by a 10% decrease does NOT return to the original. Correct method: multiply the multipliers. 10% increase = ×1.10. 10% decrease = ×0.90. Combined: 1.10 × 0.90 = 0.99 = a 1% decrease. Example: Investment gains 50% then loses 50%: $1,000 × 1.50 = $1,500, then $1,500 × 0.50 = $750. You end up with $750, not $1,000. For multiple changes, multiply all the decimal multipliers together, then use Calculator 3 to find the overall percentage change.

Grade percentage = (Points earned / Total possible points) × 100. Use Calculator 2: "X is what percent of Y?" Enter your points as X and the total as Y. Example: scored 42 out of 50 questions: (42 / 50) × 100 = 84%. For weighted grades: multiply each component score by its weight, sum all weighted scores. Example: midterm 75% (weight 40%) + final 88% (weight 60%) = (75 × 0.40) + (88 × 0.60) = 30 + 52.8 = 82.8% overall grade.