Any percentage, answered in one tap.

Seven percentage formulas, one tool

Almost every percentage question falls into one of seven cases: (1) finding a percentage of a number, (2) expressing one number as a percentage of another, (3) calculating the percentage change between two values, (4) applying a discount rate to a price, (5) adding tax to a net amount, (6) reversing tax out of a gross amount, and (7) finding margin and markup from a cost and selling price. Each case has its own tab. All calculations run entirely in your browser.

What is P% of X? (tab: X% of Y)

Enter a base value (X) and a percent (P). The tool computes X × P ÷ 100. For example, 15% of 200 is 200 × 15 ÷ 100 = 30. Use this to find tax amounts, tips, commissions, or markup values.

X is what percent of Y? (tab: Ratio)

Enter a part value (X) and a whole value (Y). The tool computes X ÷ Y × 100. For example, 45 is what percent of 180? 45 ÷ 180 × 100 = 25%. Use this to calculate achievement rates, market share, or vote share. If Y is zero, the result is undefined and no value is shown.

Percentage change from X to Y (tab: Change %)

Enter a starting value (X) and an ending value (Y). The tool computes (Y − X) ÷ |X| × 100. A positive result means an increase; a negative result means a decrease. For example: 100 to 130 gives (130 − 100) ÷ 100 × 100 = +30%; 100 to 80 gives (80 − 100) ÷ 100 × 100 = −20%. If the starting value is zero, the percentage change is undefined.

Discounted price (tab: Discount)

Enter an original price and a discount percentage. The tool computes the sale price as price × (1 − discount ÷ 100) and the amount saved as price × discount ÷ 100. For example, a $200 item at 25% off has a sale price of $150, saving $50.

Price with tax added (tab: Add tax)

Enter a net amount and a tax rate (%). The tool computes the tax asamount × rate ÷ 100 and the total as amount + tax. For example, a $100 net amount at an 8% sales tax gives $8 of tax and a $108 total. Use this for sales tax, VAT, or any add-on percentage applied to a base price.

Price with tax removed (tab: Remove tax)

Enter a gross amount (tax already included) and a tax rate (%). The tool computes the net as gross ÷ (1 + rate ÷ 100) and the tax as gross − net, splitting a tax-inclusive total back into its pre-tax amount and the tax. A $108 total at 8% reverses to a $100 net and $8 tax. This reverse-VAT calculation is the exact opposite of Add tax.

Margin and markup (tab: Margin/Markup)

Enter a cost and a selling price. The tool computes profit price − cost, margin profit ÷ price × 100, and markup profit ÷ cost × 100 at once. Selling a $60 item for $100 gives $40 profit, a 40% margin, and roughly a 66.67% markup. The key point: for the same deal, the price-based figure (margin) and the cost-based figure (markup) differ. If price is zero the margin is undefined; if cost is zero the markup is undefined, shown as a blank.

Three percentage traps people fall into

1. Stacked discounts — 30% + 10% is not 40%

Imagine a "30% off plus an extra 10% coupon" deal. Intuitively that feels like 40% off, but the real discount is about 37% of the original price. A $100 item drops to $70 after the first cut, then to $63 after the second — saving $37 (37%), not $40. The second discount applies to the already-reduced price, not the original. Plug 37% into the Discount tab and you get the same result. The mental shortcut formula: 1 − (1 − a/100) × (1 − b/100). Useful when shopping with stacking coupons or interpreting "buy more, save more" tiers.

2. Percent vs percentage points — frequently misreported

If a mortgage rate moves from 4% to 5%, that is a 1 percentage point (pp) increase — but a 25% relative change ((5 − 4) ÷ 4 × 100). A headline that says "mortgage rate up 25%" is almost always wrong. Conversely, "approval up 1%" usually means 1pp in shorthand; check the body of the article. Anywhere a percent value is itself rising or falling (interest rates, tax rates, unemployment, support rates), confusing the two distorts the apparent change. The Change % tab calculates the relative change; the FAQ summarizes the distinction in one line.

3. Averaging percentages — when the arithmetic mean lies

If a portfolio returned +50%, −50%, +50% over three years, the arithmetic mean is +16.7%, but the actual compound return is 1.5 × 0.5 × 1.5 = 1.125 — about +12.5%. More dramatic: "+100%, −50%" averages to +25% but the compound result is 1.0 — break-even. Compound returns require the geometric mean (multiplying growth factors), not the arithmetic mean. The simplest fix is to run the Change % tab on the starting value and the cumulative end value — a frequent gotcha in savings, fund, and stock comparisons.

FAQ