Percentage Calculator -- Change & Reverse

Percentage Calculator

Three modes for everyday percentage math: find amounts, identify ratios, and measure change between values. Results update in real time.

Common Scenarios

Tap any scenario to preload realistic values.

Percentage Formulas

Common Mistakes in Percentage Calculations

• Dividing by the wrong number: When calculating percentage change, always divide by the original (old) value, not the new one. Going from 80 to 100 is a 25% increase ((100-80)/80), not 20%.
• Assuming successive discounts add up: 50% off then 20% off is not 70% off. The second discount applies to the already-reduced price. 50% off $100 = $50, then 20% off $50 = $40 -- a 60% total discount.
• Confusing percentage points with percentages: If an interest rate rises from 3% to 5%, that is a 2 percentage point increase, but a 66.7% increase in the rate itself. These are very different statements.
• Reversing percentages incorrectly: If a price drops 20%, it does not take a 20% increase to get back. A $100 item at 20% off costs $80. To go from $80 back to $100 requires a 25% increase ($20/$80).
• Forgetting the base matters: 10% of 1,000 is 100, but 10% of 50 is 5. The same percentage applied to different bases produces very different absolute amounts.

Worked Examples

Frequently Asked Questions

How do I calculate a percentage of a number?

Divide the percentage by 100 and multiply by the number. The formula is: Result = (Percentage / 100) x Number. For example, 25% of 200 = (25 / 100) x 200 = 50. This is the most common percentage calculation -- used for discounts, tips, taxes, and grades.

How do I find what percentage one number is of another?

Divide the part by the whole and multiply by 100. The formula is: Percentage = (Part / Whole) x 100. For example, to find what percent 35 is of 140: (35 / 140) x 100 = 25%. This is useful for test scores, completion rates, and proportions.

How do I calculate percentage change?

Subtract the old value from the new value, divide by the absolute value of the old value, and multiply by 100. The formula is: Change = ((New - Old) / |Old|) x 100. A positive result means an increase; a negative result means a decrease. Always divide by the original (old) value.

What is the difference between percentage change and percentage difference?

Percentage change measures how much a value changed from a specific starting point -- it has a direction (increase or decrease). Percentage difference compares two values without treating either as the original. Percentage difference uses the formula: |A - B| / ((A + B) / 2) x 100. Use percentage change when one value came before the other in time; use percentage difference when comparing two independent values.

How do I reverse a percentage to find the original number?

Divide the result by the multiplier. After an increase: Original = Result / (1 + Percentage/100). After a decrease: Original = Result / (1 - Percentage/100). For example, if an item costs $72 after a 10% discount: $72 / 0.90 = $80. A common mistake is simply adding 10% back to $72, which gives $79.20 -- that is wrong because the 10% was taken from the original $80, not from $72.

Is 50% off then 20% off the same as 70% off?

No. Successive discounts do not add up directly because each discount applies to the already-reduced price. Example: $100 -> 50% off = $50 -> 20% off $50 = $40. The total discount is 60%, not 70%. To find the combined effect of successive discounts, multiply the remaining fractions: (1 - 0.50) x (1 - 0.20) = 0.40, meaning you pay 40% of the original (a 60% total discount).

How do I add a percentage to a number?

Multiply the number by (1 + percentage/100). For example, to add 15% to $200: $200 x 1.15 = $230. This works for tax, tips, markups, and salary raises. A mental shortcut: find 10% by moving the decimal one place left, then calculate 5% as half of that, and add them together. 15% of $200: 10% = $20, 5% = $10, total = $30, so $200 + $30 = $230.

What is a basis point?

A basis point (bps) is one-hundredth of a percentage point, or 0.01%. So 100 basis points = 1%. Basis points are commonly used in finance to describe small changes in interest rates, bond yields, and investment returns. For example, a rate increase from 3.50% to 3.75% is a 25 basis point increase.

How do I convert between fractions, decimals, and percentages?

Fraction to percentage: divide the numerator by the denominator and multiply by 100. For example, 3/8 = 0.375 x 100 = 37.5%. Decimal to percentage: multiply by 100. For example, 0.85 = 85%. Percentage to decimal: divide by 100. For example, 42% = 0.42.

Why does dividing by zero give an error?

The percentage formulas require dividing by the base number. If the base (denominator) is zero, the division is mathematically undefined. For example, "What percentage is 50 of 0?" has no answer. Similarly, percentage change from 0 to any value is undefined because you would divide by zero.

Does this calculator store my data?

No. All calculations run entirely in your browser using JavaScript. No inputs or results are sent to any server. Nothing is stored or logged.

Related Tools

• Discount Calculator -- calculate sale prices and savings from percentage discounts
• Tip Calculator -- figure out the right tip amount and split bills
• Percentage Change Calculator -- dedicated tool for increase and decrease calculations
• Margin Calculator -- calculate profit margins from cost and revenue
• Markup Calculator -- find the markup percentage on products

Privacy & Limitations

• Client-side only. No data is sent to any server. No cookies, no tracking of inputs or results.
• Standard precision. This calculator uses JavaScript floating-point arithmetic (IEEE 754 double precision). Results are accurate for everyday calculations but may show minor rounding in edge cases with many decimal places.
• Single calculation. Each mode performs one calculation at a time. For compound percentage problems (e.g., multiple successive discounts), calculate each step individually.

Percentage Calculator FAQ