How do you calculate the symmetric percentage difference between two values?

The symmetric percentage difference between two values is the absolute difference divided by their average: Percentage difference = |a − b| ÷ ((a + b) ÷ 2) × 100. Between 20 and 30: 10 ÷ 25 × 100 = 40%. Unlike percentage change, it does not assume either value is the 'starting' one — it treats both values symmetrically.

Percentage Calculator | Find %, % Increase/Decrease, Markup & Discount

Find a percentage of a number, work out what percent one number is of another, calculate percentage increase/decrease, markup/discount, percentage point difference, reverse percentage, and percentage difference — all in one tool, with instant, plain-English results.

Number (X)

Percent (%Y)

"What is Y% of X?" — e.g. 15% of 200. Use a period for decimals (12.5).

Part (X)

Whole (Y)

"X is what percent of Y?" — e.g. what percent is 30 of 200. Ideal for test scores, shares, or participation rates.

Old value

New value

The percentage change from the old value to the new value (increase +, decrease −).

Amount / value

Percent (%)

Add a percentage (markup) or subtract one (discount) from an amount. E.g. $100 + 20% = $120.

1st percent (%)

2nd percent (%)

Shows the point difference and the relative change between two percentages separately (e.g. 15% → 20% = 5 points, but a +33.3% relative increase).

Percent (%Y)

Value equal to this percent (Z)

"If Y% of a number is Z, what is the whole number?" — e.g. a number whose 15% is 30. Also used to recover an original price from a discounted one.

1st value

2nd value

The symmetric percentage difference between two values — use it when it's unclear which value is the "old" one. Based on the average, so it differs from increase/decrease.

1st percent (%A)

2nd percent (%B)

"What is %B of %A?" — a percentage of a percentage, for stacked/compounding rates and discounts (e.g. a 20% discount followed by an extra 10% off). Also shows the combined single-step equivalent.

Quick answer To find a percentage of a number, multiply the number by the percentage rate and divide by 100: Result = Number × Percentage ÷ 100. For example, 15% of 200 = 200 × 15 ÷ 100 = 30. To go the other way — finding what percent one number is of another — divide the part by the whole and multiply by 100.

3015% of 200

½50% = fraction equivalent

×2100% increase = 2×

0.2020% = decimal equivalent

⚙️ Note: This tool performs standard percentage arithmetic (Number × Percentage ÷ 100 and its variants); results are for informational purposes only and are not financial or investment advice. For official calculations like sales tax, loans, payroll, or inflation, use a dedicated calculator for that purpose.

🧮 Percentage Calculator — ToolPico ↗

What is a percentage, and how do you calculate one?

A complete guide — with formulas and examples — to finding a percentage of a number, percentage ratio, percentage increase/decrease, markup/discount, and percentage point difference.

A percentage (%) expresses a whole divided into 100 equal parts. Discounts, markups, interest rates, sales tax, test scores, participation rates, and most everyday statistics are expressed as percentages. Percentage calculation means quickly converting between these ratios: finding a given percentage of a number, working out what percent a part is of a whole, measuring the percentage change between two values, or adding/subtracting a percentage from an amount. You can also work backward from a known percentage to recover the whole (reverse percentage), and measure the symmetric percentage difference between two values. The calculator above handles all of these operations in separate tabs, instantly and with an explanation.

How do you find a percentage of a number?

Quick answerTo find a percentage of a number, multiply the number by the percentage rate and divide by 100: Result = Number × Percentage ÷ 100. For example, 25% of 400 = 400 × 25 ÷ 100 = 100. You get the same result by first converting the percentage to a decimal (25% = 0.25) and multiplying.

Formula: Result = Number × (Percentage ÷ 100)
Example: 15% of 200 → 200 × 0.15 = 30
Remaining portion: 200 − 30 = 170 (the 85% slice)

What percent is one number of another?

Quick answerTo find what percent a part is of a whole, divide the part by the whole and multiply by 100: Percentage = (Part ÷ Whole) × 100. For example, what percent is 30 of 200? 30 ÷ 200 × 100 = 15%. This is the most common method for test scores, participation rates, or share calculations.

This calculation answers "how much of the total does what I have represent?" A student who answers 36 of 45 questions correctly scored 36 ÷ 45 × 100 = 80%. Just enter the part and the whole in the "What % is it?" tab.

How do you calculate percentage increase?

Quick answerPercentage increase is the rise between two values relative to the starting value: Percentage increase = (New − Old) ÷ Old × 100. If a price rises from $100 to $150, the increase = (150 − 100) ÷ 100 × 100 = 50%. A negative result means a decrease, not an increase.

An important detail: a 100% increase doubles a value (100 → 200), and a 200% increase triples it (100 → 300). When calculating percentage increase, the denominator is always the old (starting) value — dividing by the new value instead gives the wrong answer.

How do you calculate percentage decrease and discounts?

Quick answerFor a decrease, the drop is measured against the old value: Decrease = (Old − New) ÷ Old × 100. For a discounted price: Discounted price = Price × (1 − Discount ÷ 100). A $250 item with a 20% discount costs 250 × 0.80 = $200, a savings of $50. To get back to the original price: 200 ÷ 0.80 = $250.

What is the difference between percent and percentage points?

Quick answerA percentage point is the absolute difference between two rates; a percentage change is that difference relative to the starting rate. If an interest rate rises from 15% to 20%, the difference is 5 percentage points, but the relative increase is (20 − 15) ÷ 15 × 100 = 33.3%. News headlines that say "rose 5 points" versus "rose 33%" describe different things — mixing them up is a common and costly mistake.

How do you find the whole when you know a percentage of it? (reverse percentage)

Quick answerIf Y% of a number is Z, divide Z by (Y ÷ 100) to find the whole: Number = Z ÷ (Percentage ÷ 100). For example, a number whose 15% is 30 → 30 ÷ 0.15 = 200. This "reverse" operation recovers an original price from a discounted one, or a whole from a known part. Just enter the percentage and the corresponding value in the "Reverse %" tab.

How do you calculate the symmetric percentage difference?

Quick answerThe symmetric percentage difference between two values is the absolute difference divided by their average: Percentage difference = |a − b| ÷ ((a + b) ÷ 2) × 100. For example, between 20 and 30: 10 ÷ 25 × 100 = 40%. Unlike percentage change, it doesn't assume which value came first (it treats both symmetrically), which is why it's used when comparing two measurements with no clear "before."

Common percentage calculations (example table)

Common percentage slices of different numbers. For exact and decimal results, use the calculator above.

10%, 20%, 25%, and 50% of a number
Number	10%	20%	25%	50%
50	5	10	12.5	25
100	10	20	25	50
200	20	40	50	100
500	50	100	125	250
1,000	100	200	250	500
1,500	150	300	375	750

Popular calculations

Related mini calculators

The three most common everyday uses of percentages: a discounted price, a tip, and sales tax. All work instantly.

🏷️Discount calculator

Apply a discount to a price and see the final amount and your savings.

Price

Discount (%)

🍽️Tip calculator

Add a tip to a bill, and optionally split it between people.

Bill amount

Tip (%)

People

🧾Sales tax calculator

Add sales tax to a price, or back it out of a tax-included total. Rates vary by state and locality — enter your own rate.

Amount

Tax rate (%)

Type

Percentage reference tables

Citable conversions: fraction–percent–decimal equivalents, percentage slices of 100, and markup/discount examples.

🔄 Live converter — type into any one field

Fraction

Percent

Decimal

Common fraction, percent, and decimal equivalents
Fraction	Percent	Decimal
1/100	1%	0.01
1/20	5%	0.05
1/10	10%	0.10
1/5	20%	0.20
1/4	25%	0.25
1/3	33.33%	0.3333
1/2	50%	0.50
3/4	75%	0.75
1/1	100%	1.00
5/4	125%	1.25
2/1	200%	2.00

Divide by 100 to convert percent to decimal; multiply by 100 to convert decimal to percent. Click any row in the table above to load it into the converter.

Percentage equivalents for 100 units
Percent	Of 100	Of 250	Of 1,000
1%	1	2.5	10
5%	5	12.5	50
8%	8	20	80
10%	10	25	100
18%	18	45	180
20%	20	50	200
25%	25	62.5	250
50%	50	125	500

Percentage of a number = Number × Percentage ÷ 100.

$100 after a markup or discount
Operation	Result	Difference
10% discount	90	−10
20% discount	80	−20
25% discount	75	−25
50% discount	50	−50
10% markup	110	+10
20% markup	120	+20
50% markup	150	+50
100% markup	200	+100

Markup: Value × (1 + Percentage ÷ 100) · Discount: Value × (1 − Percentage ÷ 100).

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Percentage terms glossary

Short definitions of the core terms used in percentage calculations.

Percent (%)A ratio expressing a whole divided into 100 equal parts. 1% equals one hundredth of the whole.

PartA portion of the whole. The numerator in a "what percent?" calculation.

Whole (base)The total value a percentage is calculated against. A percentage is always relative to a base.

Percentage increaseThe rise of a new value relative to an old one: (New − Old) ÷ Old × 100.

Percentage decreaseThe drop of a new value relative to an old one: (Old − New) ÷ Old × 100.

Percentage pointThe absolute difference between two percentage values. There are 5 points between 15% and 20%.

Decimal equivalentA percentage divided by 100. 20% = 0.20; used as a multiplier in calculations.

Fraction equivalentThe simplified fraction form of a percentage. 25% = 1/4, 50% = 1/2.

DiscountA percentage subtracted from a price. Discounted price = Price × (1 − Discount ÷ 100).

MarkupA percentage added to a value. Marked-up value = Value × (1 + Markup ÷ 100).

In-depth guides

Step-by-step explanations of the most commonly confused percentage questions.

How is 15% of 200 calculated? (step by step)

Step 1: Convert the percentage to a decimal → 15% = 15 ÷ 100 = 0.15.
Step 2: Multiply by the number → 200 × 0.15 = 30.
Step 3: Interpret → 15% of 200 is 30, and the remaining 85% is 200 − 30 = 170.

Mental-math shortcut: 15% = 10% + 5%. 10% of 200 is 20, 5% is 10; total 30. You can also see this instantly by entering 200 and 15 in the "% of number" tab above.

Don't confuse percentage increase with percentage points

When a rate rises from 15% to 20%, two different statements are both true: the difference is 5 percentage points (absolute), while the relative increase is +33.3% (the change of 20 relative to 15). In economic news, "the rate rose 5 points" describes the point difference, while "the rate rose 33%" describes the relative change.

Which one to use depends on context: use points when comparing two percentages directly, and percent when emphasizing the size of the change. The "Point difference" tab shows both at once.

Finding the original price from a discounted price

If you want the original price of an item bought for $200 after a 20% discount, divide the discounted price by (1 − discount ÷ 100): 200 ÷ 0.80 = $250. Note: adding 20% directly to $200 ($240) gives the wrong answer, because the discount was applied to $250, not $200.

The same logic applies to markups: if a marked-up price is $500 after a 25% markup, the price before markup was 500 ÷ 1.25 = $400. The "Markup / Discount" tab calculates forward; this reverse division gets you back.

Frequently asked questions

How do you calculate a percentage?

To find a percentage of a number, multiply the number by the percentage rate and divide by 100: Result = Number × Percentage ÷ 100. For example, 25% of 400 = 400 × 25 ÷ 100 = 100. You get the same result by converting the percentage to a decimal (25% = 0.25) and multiplying.

How do you find what percent one number is of another?

Divide the part by the whole and multiply by 100: Percentage = (Part ÷ Whole) × 100. For example, what percent is 30 of 200? 30 ÷ 200 × 100 = 15%. This is the most common method for test scores, participation, or share calculations.

How do you calculate percentage increase?

Percentage increase = (New − Old) ÷ Old × 100. If a price rises from $100 to $150, the increase = (150 − 100) ÷ 100 × 100 = 50%. The denominator is always the old (starting) value; dividing by the new value gives the wrong result.

How do you calculate percentage decrease / a discount?

Decrease = (Old − New) ÷ Old × 100. For a discounted price, use Price × (1 − Discount ÷ 100). A $250 item with a 20% discount: 250 × 0.80 = $200, a $50 savings. To get back to the price before the discount: 200 ÷ 0.80 = $250.

What is the difference between percent and percentage points?

Percentage point is the absolute difference between two rates; percentage change is that difference relative to the starting rate. If an interest rate rises from 15% to 20%, the difference is 5 percentage points, but the relative increase is (20 − 15) ÷ 15 × 100 = 33.3%. Mixing the two up is a common mistake.

What is 15% of 200?

15% of 200 is 30. Calculation: 200 × 15 ÷ 100 = 30. So the 15% slice of 200 is 30, and the remaining 85% slice is 170. You can also find this by converting to a decimal: 200 × 0.15 = 30.

How do you convert between percent, decimal, and fraction?

Divide by 100 to convert a percentage to a decimal: 25% = 0.25. Multiply by 100 to convert a decimal to a percentage: 0.4 = 40%. Fraction equivalents: 50% = 1/2, 25% = 1/4, 20% = 1/5, 10% = 1/10. 100% equals a whole (1).

How do you find the original price before a discount?

Divide the discounted price by (1 − discount ÷ 100). For example, an item bought for $200 after a 20% discount had an original price of 200 ÷ 0.80 = $250. The same logic in reverse gets you from a marked-up price back to the price before markup by dividing by (1 + markup ÷ 100).

A number's 15% equals 30 — what is the number? (reverse percentage)

If 15% of a number is 30, the whole number is 200. Calculation: 30 ÷ (15 ÷ 100) = 30 ÷ 0.15 = 200. General formula: Number = Value ÷ (Percentage ÷ 100). The "Reverse %" tab performs this calculation instantly.

What is the difference between percentage difference and percentage change?

Percentage change is measured against the old value: (New − Old) ÷ Old × 100. Percentage difference is measured against the average: |a − b| ÷ ((a + b) ÷ 2) × 100, and is symmetric (the result doesn't change if you swap a and b). Between 20 and 30, the change is 50% (20 → 30) or −33.3% (30 → 20), while the symmetric percentage difference is 40% either way.

How do you find a percentage of a percentage (stacked discounts or compounding rates)?

To find B% of A%, multiply the two percentages and divide by 100: Result = A × B ÷ 100. For example, 10% of 20% = 20 × 10 ÷ 100 = 2%. This is different from applying two percentages one after another — like a 20% discount followed by an extra 10% off — which is not simply 30% off. The combined, stacked effect uses (1 + A ÷ 100) × (1 + B ÷ 100) × 100 − 100, which works out to 28% off overall, because the second discount applies to the already-reduced price. The "% of a %" tab calculates both at once.

Methodology & sources

ToolPico's Percentage Calculator is a free, independent tool. The calculation engine performs every operation with standard arithmetic formulas: percentage of a number is Number × Percentage ÷ 100, percentage ratio is Part ÷ Whole × 100, percentage change is (New − Old) ÷ Old × 100, markup/discount is Value × (1 ± Percentage ÷ 100), percentage point difference is |Percentage₂ − Percentage₁|, reverse percentage is Value ÷ (Percentage ÷ 100), and symmetric percentage difference is |a − b| ÷ ((a + b) ÷ 2) × 100. Results are computed instantly client-side (in your browser); no data is sent to a server.

Basis: Standard mathematics (ratio and proportion). Last updated: July 19, 2026. Results are for informational purposes only and do not constitute financial or investment advice; for official calculations, consult the relevant agency or a qualified professional.

Percentage Calculator

What is a percentage, and how do you calculate one?

How do you find a percentage of a number?

What percent is one number of another?

How do you calculate percentage increase?

How do you calculate percentage decrease and discounts?

What is the difference between percent and percentage points?

How do you find the whole when you know a percentage of it? (reverse percentage)

How do you calculate the symmetric percentage difference?

Common percentage calculations (example table)

Popular calculations

Related mini calculators

Percentage reference tables

Add this calculator to your site (embed code)

Percentage terms glossary

In-depth guides

Frequently asked questions

Methodology & sources

🔗 Add this tool to your site