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Percentage Calculator

Calculate percentages instantly: what is X% of Y, percentage increase or decrease, reverse percentages, and percentage difference. Free online tool with step-by-step formulas.

Last revised 25 September 2026

By Team GlobalCalqulate · About our editorial standards

Percentage Calculation

Calculation Type

Value X

Meaning depends on the mode above: the percentage (for 'X% of Y', increase/decrease is X→Y instead, reverse percentage), or the first number (for 'what % is X of Y' and percentage difference). A change from a starting value of zero, or a percentage of a whole of zero, is mathematically undefined, so the calculator reports it instead of returning a number.

Value Y

For 'Reverse Percentage', enter the value AFTER the percentage change (e.g. the discounted price). For increase/decrease, enter the new/final value.

Decimal Places

Result

200.00

(20 / 100) × 1000

Methodology

Formula:: X% of Y
Content last updated:: September 2026
Scheduled re-verification:: September 2027

Calculation type: Exact calculation.

Formula & methodology

Formula used

X% of Y

result = (X ÷ 100) × Y

Converts the percentage to a decimal and multiplies.

X is what percent of Y

result = (X ÷ Y) × 100

Expresses X as a share of Y. Undefined when Y is zero, which the calculator reports rather than guessing.

Percentage increase or decrease

change = ((new − old) ÷ old) × 100

Change is always measured against the ORIGINAL value. This is why a 50% fall followed by a 50% rise does not return to the starting point.

Variable definitions

Symbol	Meaning	Unit
X	First value. the percentage, or the part, depending on the mode	—
Y	Second value. the base or whole	—

Step-by-step calculation

1. Choose what you are calculating
Each mode uses a different formula, shown alongside the result.
2. Enter the two values
The working is displayed so the result can be checked by hand.
3. Set the rounding
Rounding is applied only for display; the calculation runs at full precision.

Limitations

Percentage change is undefined when the original value is zero, and misleading when it is very small — a rise from 0.01 to 0.02 is a 100% increase but a trivial absolute change.
Percentage point and percent are not the same. A rate moving from 4% to 6% is a rise of 2 percentage points, but a 50% increase.
Successive percentage changes do not add. Applying −50% then +50% leaves you 25% below where you started.

This page is educational. It applies the formula described above to the figures you enter and shows the arithmetic behind the result. The output is only as good as the inputs and the assumptions listed here, and it is general information rather than advice about your particular situation.

Help & FAQs

Frequently Asked Questions

Clear answers to common questions to help you use this calculator confidently.

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

Tap to view the answer

Divide the part by the whole, then multiply by 100. Formula: (Part ÷ Whole) × 100 = %. Example: What % is 25 of 200? (25 ÷ 200) × 100 = 12.5%.

What is the formula for percentage increase or decrease?

Tap to view the answer

Percentage change = ((New Value − Old Value) ÷ Old Value) × 100. A positive result is an increase, a negative result is a decrease. Example: salary increased from 50,000 to 60,000: ((60000 − 50000) ÷ 50000) × 100 = 20% increase.

How do I find the original price after a discount?

Tap to view the answer

Formula: Original Price = Final Price ÷ (1 − Discount%). Example: an item costs 600 after a 25% discount. 600 ÷ (1 − 0.25) = 600 ÷ 0.75 = 800 original price.

What's the difference between a percentage point and a percentage?

Tap to view the answer

A percentage point is the absolute (simple) difference between two percentages. A percentage is the relative change. Example: going from 5% to 7% is +2 percentage points, but a 40% relative increase (2/5 = 40%).

Why does a 50% decrease require a 100% increase to recover?

Tap to view the answer

Because you lose 50% of the original value, then need 100% of the new (smaller) value just to get back to where you started. In general, Recovery % = (X ÷ (100 − X)) × 100 for an X% decrease.

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How to Use This Calculator

Choose What to Calculate

Select from six common percentage scenarios: find X% of Y, what percent X is of Y, increase/decrease, reverse percentages, or percentage difference.

Enter Your Numbers

Input values for X and Y. For 'What is 20% of 1000?', enter 20 and 1000. For increase/decrease, enter old and new values.

View Results

Get the answer, the formula used, and step-by-step workings so you understand exactly how the calculation was done.

Understanding Your Results

Percentage
A part per hundred: (Part ÷ Whole) × 100. 20% means 20 out of every 100, or 0.20 as a decimal.
% Increase
((New − Old) ÷ Old) × 100. Measures growth. 100 → 120 = 20% increase.
% Decrease
((Old − New) ÷ Old) × 100. Measures decline. 100 → 80 = 20% decrease.
Reverse %
Found when you know a percentage change and the value it produced. Original = Final ÷ (1 − Rate/100), where Rate is positive for a discount/decrease and negative for a markup/increase.

Key Tips

✓
10% of any number = divide by 10. 20% = double that. 5% = half of 10%.
✓
Percentage difference uses the average as base: |A−B| ÷ ((A+B)/2) × 100. Different from percentage change.
✓
When calculating a discount, subtract the discount from 1: 25% off = multiply by 0.75.
✓
A 50% loss requires a 100% gain to recover. If $100 drops to $50 (−50%), you need +100% to get back to $100.

How Percentages Work

The Basic Percentage Formula

Percentage = (Part ÷ Whole) × 100. To find 20% of 1,000: Part = 20/100 × 1,000 = 200. To find what percent 200 is of 1,000: Percent = (200 ÷ 1,000) × 100 = 20%. The calculator handles six common variations so you don't need to remember which formula to apply.

Percentage Change — Increase and Decrease

Percentage change answers: 'How much did this number go up or down, relative to where it started?' The formula is ((New − Old) ÷ Old) × 100. A positive result means increase; negative means decrease. This is different from percentage difference, which compares two numbers without direction using their average as the base. Use percentage change for tracking growth (revenue, prices, test scores); use percentage difference when comparing two independent values.

Reverse Percentage Calculations

Sometimes you know the value after a percentage change and need to find the original. If an item costs $600 after a 25% discount: Original = $600 ÷ (1 − 0.25) = $600 ÷ 0.75 = $800. Enter the percentage as a positive number for a decrease/discount, or a negative number for an increase/markup — for example, enter −10 to reverse a 10% markup.

Quick Mental Math Shortcuts

10% = divide by 10. 5% = divide by 20. 25% = divide by 4. 50% = divide by 2. 1% = divide by 100. For 15%, add 10% + 5%. These shortcuts build number sense even when using a calculator.

Common Percentage Mistakes

Percentage point vs. percentage change: if an interest rate goes from 5% to 6%, that's a 1 percentage point increase, but a 20% relative increase — the two phrasings mean different things and are often confused. Assuming increases and decreases cancel out: a 50% increase followed by a 50% decrease does NOT return to the original value (100 → 150 → 75, not 100), because the second percentage is taken from a different base. Stacking discounts by simple addition: "30% off, plus an extra 20% off" is not 50% off — apply them sequentially (100 → 70 → 56, a 44% total discount, not 50%). Confusing "X% of Y" with "X% more than Y": 20% of 50 is 10, but 20% more than 50 is 60.

Percentage Change Is Not Symmetric

A decrease requires a larger percentage increase to reverse it than the size of the original decrease. If a value drops 50% (100 → 50), it takes a 100% increase — not 50% — to get back to 100, because the increase is calculated from the smaller post-decrease base. This asymmetry is why a 50% loss followed by a 50% gain leaves you worse off than where you started (100 → 50 → 75).

Formula & methodology

Formula used

X% of Y

result = (X ÷ 100) × Y

Converts the percentage to a decimal and multiplies.

X is what percent of Y

result = (X ÷ Y) × 100

Expresses X as a share of Y. Undefined when Y is zero, which the calculator reports rather than guessing.

Percentage increase or decrease

change = ((new − old) ÷ old) × 100

Change is always measured against the ORIGINAL value. This is why a 50% fall followed by a 50% rise does not return to the starting point.

Variable definitions

Symbol	Meaning	Unit
X	First value. the percentage, or the part, depending on the mode	—
Y	Second value. the base or whole	—

Step-by-step calculation

1. Choose what you are calculating
Each mode uses a different formula, shown alongside the result.
2. Enter the two values
The working is displayed so the result can be checked by hand.
3. Set the rounding
Rounding is applied only for display; the calculation runs at full precision.

Limitations

Percentage change is undefined when the original value is zero, and misleading when it is very small — a rise from 0.01 to 0.02 is a 100% increase but a trivial absolute change.
Percentage point and percent are not the same. A rate moving from 4% to 6% is a rise of 2 percentage points, but a 50% increase.
Successive percentage changes do not add. Applying −50% then +50% leaves you 25% below where you started.

How Percentages Work

The Basic Percentage Formula

Percentage Change — Increase and Decrease

Reverse Percentage Calculations

Quick Mental Math Shortcuts

10% = divide by 10. 5% = divide by 20. 25% = divide by 4. 50% = divide by 2. 1% = divide by 100. For 15%, add 10% + 5%. These shortcuts build number sense even when using a calculator.

Calculator inputs

Percentage Calculation

Your results

Methodology

Formula & methodology

Formula used

X% of Y

X is what percent of Y

Percentage increase or decrease

Variable definitions

Step-by-step calculation

Limitations

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

What is the formula for percentage increase or decrease?

How do I find the original price after a discount?

What's the difference between a percentage point and a percentage?

Why does a 50% decrease require a 100% increase to recover?

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Calculator inputs

Percentage Calculation

Your results

Methodology

How to Use This Calculator

Example: What is 20% of $1,000?

Understanding Your Results

Key Tips

How Percentages Work

The Basic Percentage Formula

Percentage Change — Increase and Decrease

Reverse Percentage Calculations

Quick Mental Math Shortcuts

Common Percentage Mistakes

Percentage Change Is Not Symmetric

Formula & methodology

Formula used

X% of Y

X is what percent of Y

Percentage increase or decrease

Variable definitions

Step-by-step calculation

Limitations

How to Use This Calculator

Example: What is 20% of $1,000?

Understanding Your Results

Key Tips

How Percentages Work

The Basic Percentage Formula

Percentage Change — Increase and Decrease

Reverse Percentage Calculations

Quick Mental Math Shortcuts

Common Percentage Mistakes

Percentage Change Is Not Symmetric