Percentage Calculator

What is X% of a number, what percent one value is of another, the whole behind a known percentage, the rise or fall between two figures, and sale prices after a discount — all on one page.

Calculation
Results
X% of the value
Value increased by X%
Value decreased by X%
Fill in both fields — results update as you type.

Every calculation happens in your browser — the numbers you type never leave your device.

FAQ

How is the percentage change worked out?

The difference between the new and old value is divided by the old value: (new − old) ÷ old × 100. A positive result is a rise, a negative one a fall. Going from 200 to 250 is +25%, while 250 back to 200 is −20% — the base changes, so the two directions aren’t symmetric.

How do I work out a sale price?

Pick the Discount mode, enter the original price and the percent off. You’ll see what you pay and what you keep in your pocket — 20% off an $80 item leaves $64 to pay and $16 saved.

Why doesn’t +10% followed by −10% get back to the start?

Each step is measured against a different base. Adding 10% to 100 gives 110, but 10% of 110 is 11, so subtracting it lands at 99 — not 100. The larger the percentage, the wider that gap becomes.

Is going from 10% to 12% a 20% change or 2 percentage points?

Both, describing different things. The % change mode reports the relative change (a 20% increase, since 2 is 20% of 10). The gap itself — 2 percentage points — is a separate, absolute figure. Always check which one a report or comparison means.

Written and reviewed by the BroBroGo editorial team.Last updated:

Percentages are a fundamental mathematical concept used to express a fraction of 100. Whether you are a student completing schoolwork, a shopper calculating savings on a sale item, or someone comparing data points, understanding how percentages work is essential for everyday decisions.

The Percentage Calculator simplifies these tasks by performing calculations directly in your web browser. No data is uploaded to an external server; every calculation happens in your browser, meaning the numbers you type never leave your device. The tool processes inputs in real time, updating the results as you type once both required fields are filled.

Calculating a Percentage of a Given Number

Finding a specific percentage of a base value is one of the most common mathematical operations. This calculation determines what a fractional portion of a number represents in absolute terms.

The Mathematical Formula

To find a percentage of a number, multiply the base value by the percentage and divide by 100:

Result = (Base Value × Percentage) / 100

To find the value increased or decreased by a percentage, the formulas are:

Increased Value = Base Value × (1 + Percentage / 100)

Decreased Value = Base Value × (1 - Percentage / 100)

Using the Tool

In this mode, you provide two inputs:

  • Percentage (%)
  • Of this value

Once both fields contain valid numbers, the tool displays three distinct outputs:

  • X% of the value
  • Value increased by X%
  • Value decreased by X%

If you enter an input that is not a number, the tool displays the error message: "That is not a valid number". Additionally, all numerical inputs must be kept under a quadrillion (10¹⁵); exceeding this limit triggers the error: "These numbers are too large — keep them under a quadrillion".

Determining What Percentage One Number Is of Another

When comparing two quantities, you often need to express the smaller or larger portion as a share of the whole. This calculation identifies the ratio between a part and a base value, scaled to a percentage.

The Mathematical Formula

To find what percentage a part is of a whole, divide the part by the whole and multiply by 100:

Percentage = Part / Whole × 100

Using the Tool

To perform this calculation, enter the following inputs:

  • This value
  • As a share of

The tool will output the calculated Percentage.

A mathematical edge case occurs if the base value is zero, as division by zero is undefined. If you enter 0 in the As a share of field, the tool displays the error message: "A share of zero is undefined — the second value can’t be 0".

Calculating Percentage Increase and Decrease

Measuring the relative change between an old value and a new value is crucial when tracking growth, inflation, or financial performance.

The Mathematical Formula

The percentage change is calculated by finding the absolute difference between the new value and the old value, dividing that difference by the old value, and multiplying by 100:

Percentage Change = (New Value - Old Value) / Old Value × 100

Using the Tool

To find the change between two points, enter:

  • From (old value)
  • To (new value)

The tool generates two outputs:

  • Change (expressed as a percentage)
  • Difference (the absolute numerical change)

Rules and Edge Cases

  • Identical Values: If the old and new values are the same, the tool outputs: "The two values are identical — no change".
  • Starting from Zero: If the From (old value) field is set to 0, a percentage change cannot be calculated. The tool displays the error: "Change from zero has no percentage — the old value can’t be 0".

Understanding the Asymmetry of Percentage Changes

A common point of confusion in mathematics is the directional asymmetry of percentage changes. Because the base value changes depending on the direction of the calculation, a percentage increase followed by the same percentage decrease does not return you to the starting number.

For example, if you start with 100 and add 10%, you get 110. However, if you then subtract 10% from 110, you must calculate 10% of 110 (which is 11). Subtracting 11 from 110 leaves you with 99, not your original 100. The larger the percentage used, the wider this gap becomes.

Similarly, going from 200 to 250 is a +25% increase (since the difference of 50 is 25% of the starting value, 200). Conversely, moving from 250 back to 200 is a −20% decrease, because the difference of 50 is now measured against the new starting value of 250.

Calculating Discounts and Sale Prices

Determining savings and final prices during a sale is a highly practical everyday application of percentages.

The Mathematical Formula

To calculate how much you save and the final price of a discounted item, use the following formulas:

You Save = (Original Price × Discount Percentage) / 100

Final Price = Original Price - You Save

Using the Tool

To find your savings, input:

  • Original price
  • Discount (%)

The tool provides two outputs:

  • Final price
  • You save

A discount percentage must represent a realistic reduction. If you enter a discount value that is less than 0 or greater than 100, the tool displays the error message: "A discount must be between 0 and 100 percent".

Frequently Asked Questions

Is going from 10% to 12% a 20% change or 2 percentage points?

Both, describing different things. The % change mode reports the relative change (a 20% increase, since 2 is 20% of 10). The gap itself — 2 percentage points — is a separate, absolute figure. Always check which one a report or comparison means.

How is the percentage change worked out?

The difference between the new and old value is divided by the old value: (new − old) ÷ old × 100. A positive result is a rise, a negative one a fall. Going from 200 to 250 is +25%, while 250 back to 200 is −20% — the base changes, so the two directions aren’t symmetric.

How do I work out a sale price?

Pick the Discount mode, enter the original price and the percent off. You’ll see what you pay and what you keep in your pocket — 20% off an $80 item leaves $64 to pay and $16 saved.

Why doesn’t +10% followed by −10% get back to the start?

Each step is measured against a different base. Adding 10% to 100 gives 110, but 10% of 110 is 11, so subtracting it lands at 99 — not 100. The larger the percentage, the wider that gap becomes.

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