Calculate Percentages
Instantly

To calculate a percentage of a number, multiply the number by the percentage and divide by 100. For example, to find 20% of 150: multiply 150 × 20 = 3,000, then divide by 100 = 30. Alternatively, convert the percentage to a decimal (20% = 0.20) and multiply: 150 × 0.20 = 30. This method works for any percentage calculation, whether you're calculating discounts, tips, taxes, or any other percentage-based value.

The percentage increase formula is: ((New Value - Original Value) ÷ Original Value) × 100. For example, if a price increases from $50 to $75, the calculation is: ((75 - 50) ÷ 50) × 100 = (25 ÷ 50) × 100 = 0.5 × 100 = 50% increase. This formula is essential for calculating price changes, salary raises, growth rates, and investment returns. Always subtract the original from the new value first, then divide by the original value.

To calculate percentage decrease: 1) Find the difference between original and new value (Original - New). 2) Divide the difference by the original value. 3) Multiply by 100 to get the percentage. Example: Price drops from $80 to $60. Step 1: 80 - 60 = 20. Step 2: 20 ÷ 80 = 0.25. Step 3: 0.25 × 100 = 25% decrease. This method is perfect for calculating discounts, depreciation, weight loss, or any reduction in value.

To find what percent X is of Y, use the formula: (X ÷ Y) × 100. For instance, to find what percent 25 is of 200: (25 ÷ 200) × 100 = 0.125 × 100 = 12.5%. This calculation is useful for determining test scores (85 out of 100 = 85%), completion rates, market share, or any scenario where you need to express one value as a percentage of another. Always divide the partial value by the total value.

To calculate discount percentage: 1) Subtract the sale price from the original price to find the discount amount. 2) Divide the discount amount by the original price. 3) Multiply by 100. Example: Original price $120, sale price $90. Discount amount: $120 - $90 = $30. Discount percentage: ($30 ÷ $120) × 100 = 25% off. This helps you compare deals, understand savings, and make informed shopping decisions.

Reverse percentage calculation finds the original value when you know the final value and percentage. Formula: Original Value = Final Value ÷ (1 + Percentage/100) for increases, or Original Value = Final Value ÷ (1 - Percentage/100) for decreases. Example: If a price after 20% tax is $120, the original price is: $120 ÷ 1.20 = $100. This is crucial for calculating pre-tax amounts, original prices before discounts, or base salaries before raises.

To add a percentage to a number: 1) Convert the percentage to decimal (divide by 100). 2) Multiply the original number by (1 + decimal). Or use: Original × (1 + Percentage/100). Example: Add 15% to $200. Method 1: 15% = 0.15, so $200 × 1.15 = $230. Method 2: $200 × (1 + 15/100) = $200 × 1.15 = $230. This is used for calculating prices with tax, salary increases, markup pricing, and growth projections.

To calculate percentage difference between two numbers: 1) Find the absolute difference (larger - smaller). 2) Find the average of the two numbers. 3) Divide the difference by the average. 4) Multiply by 100. Formula: |A - B| ÷ ((A + B)/2) × 100. Example: Compare 80 and 100. Difference: 20. Average: 90. Percentage difference: 20 ÷ 90 × 100 = 22.22%. This method is ideal for comparing values without a clear 'before' and 'after' relationship.

Compound percentage applies multiple percentage changes sequentially. Formula: Final = Initial × (1 + %1/100) × (1 + %2/100)... Example: $100 increased by 10% then 20%. Step 1: $100 × 1.10 = $110. Step 2: $110 × 1.20 = $132. Total increase is 32%, not 30%! This is crucial for understanding compound interest, multi-year growth rates, sequential price changes, and investment returns. Each percentage is applied to the result of the previous calculation.

To calculate tip percentage quickly: 1) For 20% tip: Divide bill by 5. 2) For 15% tip: Divide bill by 10, then add half of that. 3) For 10% tip: Divide bill by 10. Example on $80 bill: 20% = $80 ÷ 5 = $16. 15% = $8 + $4 = $12. 10% = $8. Mental math trick: Move decimal one place left for 10%, double it for 20%. These shortcuts help you calculate tips instantly without a calculator.

To calculate sales tax: 1) Multiply the purchase amount by the tax rate (as a decimal). 2) Add the tax to the original amount for the total. Formula: Tax = Price × (Tax Rate/100), Total = Price + Tax. Example: $50 item with 8.5% tax. Tax amount: $50 × 0.085 = $4.25. Total price: $50 + $4.25 = $54.25. To find tax rate from total: Tax Rate = ((Total - Subtotal) ÷ Subtotal) × 100.

Percentage error measures the accuracy of a measurement or estimate. Formula: |Actual Value - Expected Value| ÷ |Expected Value| × 100. Example: You estimate 250 people will attend an event, but 280 actually come. Error: |280 - 250| ÷ 250 × 100 = 30 ÷ 250 × 100 = 12% error. The absolute value ensures error is always positive. This is essential in science, forecasting, quality control, and any field requiring precision measurement.

To calculate percentage of total in Excel: 1) Divide the part by the total using formula =Part/Total. 2) Format as percentage (Ctrl+Shift+%). Example: If cell A1 contains 25 and B1 contains 200, enter =A1/B1 in C1, which gives 0.125 or 12.5%. For running totals: =A2/SUM($A$2:$A$10). The dollar signs create absolute references. Excel automatically multiplies by 100 when you apply percentage formatting. Use for budgets, sales analysis, and data reports.

Markup and margin are different: Markup = ((Selling Price - Cost) ÷ Cost) × 100. Margin = ((Selling Price - Cost) ÷ Selling Price) × 100. Example: Cost $50, Selling Price $75. Markup: (($75 - $50) ÷ $50) × 100 = 50% markup. Margin: (($75 - $50) ÷ $75) × 100 = 33.33% margin. Markup is based on cost (how much you add), margin is based on selling price (your profit percentage). Retailers use markup for pricing, while investors focus on margin.

To calculate percentage change over time, use: ((End Value - Start Value) ÷ Start Value) × 100 ÷ Number of Time Periods = Average % Change per Period. For compound annual growth rate (CAGR): ((End Value ÷ Start Value)^(1/Years) - 1) × 100. Example: Investment grows from $1,000 to $1,500 over 3 years. Simple: 50% ÷ 3 = 16.67% per year average. CAGR: ((1,500 ÷ 1,000)^(1/3) - 1) × 100 = 14.47% annual compound growth.