Percentage Calculator

Find a Percentage or Part of an Amount

To find what percentage one amount is of another, divide the part by the whole and multiply by 100. In a fraction, the numerator is the top number and the denominator is the bottom number. For example, 3/8 × 100 = 37.5%.

The default calculation is 200 / 800 × 100 = 25%. To find 25% of 800, use the percentage-of-an-amount mode: 800 × 25 / 100 = 200. The first calculation finds a rate. The second finds an amount.

The Australian Bureau of Statistics explanation of percentages uses the same part-to-whole calculation. A zero denominator has no defined percentage, even when the numerator is also zero.

For 1/8, divide 1 by 8 to get the exact decimal 0.125, then multiply by 100 to get 12.5%. Dividing 12.5% by 100 returns 0.125. Percentage-to-fraction mode reduces 12.5/100 to 1/8.

Count-based chance divides favourable outcomes by all equally weighted outcomes. One favourable outcome among eight gives 12.5%. This assumes each outcome has the same weight. A count ratio does not predict a legal outcome.

Percentage frequency divides the category count by the total observation count. If 20 of 100 transactions are cash withdrawals, their count share is 20%. Their share of total money depends on the withdrawal amounts. An empty observation set has no defined percentage frequency.

Once you have chosen an allocation percentage, use the property settlement calculator to apply it to a complete property pool.

Amounts accept zero or magnitudes from 0.000000001 to 1 trillion. Percentage inputs accept magnitudes up to 1 million. Enter amounts in the same units.

Results display up to two decimal places, so decimal equivalents can be rounded. Very small nonzero results retain two significant figures. Calculations use unrounded values. An amount result keeps your input units. Round monetary amounts to cents when preparing the final schedule.

Calculate an Increase or Difference

Percentage change uses a starting amount: (end − start) / start × 100. Moving from $100 to $120 is a 20% increase. Reversing the amounts is a 16.67% decrease because the starting base becomes $120. The Central Statistics Office percentage-change method explains this starting-base formula.

Symmetric percentage difference compares two non-negative amounts without choosing a starting point: absolute difference divided by their mean, multiplied by 100. For $100 and $120, the mean is $110 and the difference is 18.18%. Swapping the amounts leaves that result unchanged. Two zero amounts have no defined percentage difference.

For growth, use the earlier amount as the base. For a discount, use the original price. Profit divided by cost gives the markup percentage. Divide profit by sales to find the margin. A $20 profit on $100 cost and $120 sales gives 20% markup and 16.67% margin.

A salary rising from $80,000 to $84,000 increases by 5%, using the original $80,000 as denominator. A price falling from $250 to $225 has a 10% discount. Year-on-year sales rising from $200,000 to $230,000 grow by 15%, using the prior year’s $200,000.

Gross profit margin divides revenue less cost of sales by revenue. For one reporting period, $120,000 revenue less $80,000 cost of sales gives $40,000 gross profit. Gross profit margin is 33.33%. Markup on that cost is 50%. The phrase “profit percentage” needs a stated denominator to distinguish these figures.

Overhead ratio divides overhead expenses by the selected revenue or cost base for the same period. Overheads of $15,000 against revenue of $100,000 give 15%. Selecting a $60,000 cost base gives 25%. Identify which expenses count as overheads and use a consistent accounting basis.

A rate rising from 20% to 25% changes by five percentage points and increases by 25% relative to its old rate. These are different measures. For a negative starting amount, this tool retains the signed denominator and states that convention beside the result. A positive movement from -100 to -80 therefore calculates as -20% and must not be described as a 20% decline.

Reverse a Percentage

Recover an original amount by dividing the final amount by 1 + change / 100. Enter a negative change for a reduction. A final $120 after a 20% increase gives $120 / 1.2 = $100. A final $80 after a 20% reduction gives $80 / 0.8 = $100.

Adding 20% to $100 gives $120. Subtracting 20% from $120 gives $96 because the second percentage uses a larger base. To undo the increase, divide by 1.2.

A 100% reduction leaves zero and removes the information needed to recover the original amount. Reverse mode rejects -100% and lower changes. Add-or-subtract mode accepts a 100% reduction and rejects larger reductions.

Check Average Percentages and Error

Weight percentages by the amounts behind them when those bases differ. An illustrative schedule has 10% of $100 and 20% of $300. The combined part is $10 + $60 = $70, across a $400 base, giving 17.5%. The simple average of the two rates is 15% and treats the unequal bases as equal.

Weighted-average mode uses sum of (percentage × weight) divided by sum of weights. Enter 10,100 on one row and 20,300 on the next to reproduce 17.5%. A weight can be zero, but at least one must be positive. Negative weights are rejected. Equal weights calculate the simple average.

Absolute percentage error is |observed − expected| / |expected| × 100. An observed $98 against an expected $100 gives 2% error. This measure reports the size of the error without its direction and uses the magnitude of a negative expected amount. An expected amount of zero has no defined percentage error. Report the amount difference instead.

Relative uncertainty expresses an entered absolute uncertainty as a share of the reported amount’s magnitude. An amount of $250 with uncertainty of $5 gives 5 / 250 × 100 = 2%. A reported amount of -$250 gives the same 2% magnitude. Zero absolute uncertainty gives 0% when the reported amount is nonzero.

Percentage error compares an observation with an expected value. Relative uncertainty uses the uncertainty you supply, without assuming an expected value. This conversion alone establishes no statistical confidence interval. A reported amount of zero has no defined relative uncertainty.

Signed variance uses (actual − expected) / expected × 100, available through percentage-change mode with expected as the starting amount. Absolute-error mode removes the sign. For $98 against $100, signed variance is -2% and absolute error is 2%.

One row per percentage, then a comma and its weight. For 10% of a base of 100, enter 10,100. Use the same units for all weights. Maximum 500 rows.

Check the Formula in a Calculator or Excel

A handheld calculator can reproduce each result with division and multiplication. For 200 out of 800, enter 200 ÷ 800 × 100 = to get 25. For 25% of 800, enter 800 × 25 ÷ 100 = to get 200.

For the change from 100 to 120, enter (120 − 100) ÷ 100 × 100 = to get 20%. Symmetric difference instead uses |120 − 100| ÷ ((100 + 120) ÷ 2) × 100 =, giving 18.18%. Without an absolute-value button, subtract the smaller amount from the larger.

In Excel, put the part or starting amount in A2 and the whole or ending amount in B2. Enter =A2/B2 for part-to-whole percentage, =(B2-A2)/A2 for directional change and =ABS(B2-A2)/AVERAGE(A2,B2) for symmetric difference.

Format those Excel cells as Percentage with two decimal places. With A2 = 100 and B2 = 120, they show 83.33%, 20% and 18.18% respectively. Keep the formula’s denominator nonzero. Symmetric difference here uses non-negative amounts.

To add 20% to an amount in A2, enter =A2*(1+20%). The formula =A2*25% finds 25% of A2. Microsoft’s Excel percentage instructions explain percentage formatting and calculation.

The arithmetic is reproducible whether you use a handheld calculator or look for an Omni or Google percentage calculator. This page applies the formulas above and has no affiliation with those providers.

Compare Financial Ratios and Time Shares

Occupancy percentage is occupied periods divided by available periods, multiplied by 100. If a property is occupied for 80 of 100 available nights, occupancy is 80%. Use the same unit and define which periods are available.

For billable time, 24 billable hours out of 40 available hours is 60%. Convert minutes to hours before mixing entries, or keep both figures in minutes. A rate moving from 60% to 65% gains five percentage points. Its relative increase is 8.33%.

Elapsed-year mode divides calendar days elapsed by 365 or 366. Select the year and endpoint. Exclude counts to the start of the endpoint day. Include counts through its end. The count always starts with the first day of the selected year.

In leap year 2024, the start of 2 Jul follows 183 elapsed days, giving 183 / 366 × 100 = 50%. Including 1 Jul gives the same count. The US Naval Observatory leap-year rule includes years divisible by four, except century years unless divisible by 400.

For supplied day counts or other part-year periods, use time-or-occupancy mode. An entered 182 of 365 days gives 49.86%. State which endpoints your counts include. A time share measures elapsed or occupied time and does not forecast annual financial performance.

Food-cost percentage divides food cost by the relevant food sales for the same period. An illustrative $12,000 food cost against $40,000 food sales gives 30%. In proportion mode, enter 12000 as the part and 40000 as the whole. State whether cost includes waste, stock movements or staff meals. Use the same GST basis for both amounts before interpreting the ratio.