Percentage Calculator | OverCalculator

What Is a Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It’s a convenient, unit-free way to compare two quantities. Whenever you see the symbol ”%” (or the words “percent” or “pct”), it indicates “out of 100.” Converting between percentages, fractions, and decimals is straightforward:

35% = 0.35 as a decimal
35% = 35/100 as a fraction

Calculating a Percentage

To calculate a percentage, multiply the ratio by 100. For example, if 25 out of 50 students are male:

25 / 50 = 0.5
0.5 × 100 = 50%

Hence, half of the class (50%) is male.

The Percentage Formula

Three main elements come into play when working with percentages:

(P): The percentage
(V_1): The initial value
(V_2): The resulting value

They relate by:

P \times V_1 = V_2

If solving for (V_2), you do
$V_2 = P \times V_1$
where (P) is in decimal form.
If solving for (P), you rearrange to
$P = \frac{V_2}{V_1} \times 100.$

For instance:

P × 30 = 1.5
P = 1.5 / 30 = 0.05 = 5%

If you solve for (P) manually, remember to multiply by 100 to convert from a decimal to a percent.

The Percentage Difference Formula

The percentage difference between two values is found by taking the absolute difference between them, dividing by their average, then multiplying by 100:

\text{Percentage Difference} = \frac{\lvert V_1 - V_2 \rvert}{\frac{V_1 + V_2}{2}} \times 100

Example:

|10 - 6| = 4
(10 + 6)/2 = 8
4 / 8 = 0.5 = 50%

The Percentage Change Formula

Percentage change (increase or decrease) compares how much a value has risen or fallen relative to its initial value.

Calculate the difference:
$\text{difference} = \lvert V_2 - V_1 \rvert$
Compare to the original value:
$(\text{difference} / V_1) \times 100$

Practical Examples

If you want to increase 500 by 10%:

500 × (1 + 0.1) = 550

If you want to decrease 500 by 10%:

500 × (1 – 0.1) = 450

How To Use a Percentage Calculator

A percentage calculator can answer questions like:

What percent of X is Y?
What is p% of X?
X is p% of what?
By how much does X change if it’s increased/decreased by p%?

Simply plug in two known values, and it calculates the third automatically.

Example 1: What Is p% of X?

Enter the percentage (p).
Enter the number (X).
The calculator returns (p%) of (X).

Example: If you scored 80% on a 30-mark test, your score is (0.8 \times 30 = 24) marks.

Example 2: X Is What Percent of Y?

Enter the number (X).
Enter the number (Y).
The calculator returns the percentage.

Example: If Gavin’s rent is $1245 and his monthly budget is $4000:

(1245 / 4000) × 100 ≈ 31.125%

Example 3: X Is p% of What?

Enter the number (X).
Enter the known percentage (p).
The calculator returns the original value.

Example: 10 is 5% of what number?

10 = 0.05 × ?
? = 10 / 0.05 = 200

Example 4: What Is X Increased/Decreased by p%?

Enter the initial value (X).
Select increase or decrease.
Enter the percentage (p).
The calculator shows the new value.

Example: If a candy bar costing $5 increases by 30%:

5 × (1 + 0.3) = 6.50

Why Percentages Are Everywhere

Percentages show up in all areas of life:

Shopping discounts: “50% OFF!” signs.
Finance: Income tax rates, sales tax, interest rates.
Health: Body fat percentage, daily nutritional values.
Academics: Exam scores, statistical data.
Science: Concentrations, efficiency, rates of change.

They are simply an efficient way to compare parts of a whole—expressed on a scale of 0 to 100.

More About Percentages

What Does 1% Mean?

1% means one hundredth (

\frac{1}{100}

). So, 5% = 5/100 = 0.05.

If you have 20 cookies, 40% of them is:

(40 / 100) × 20 = 8

Decimal Fractions and Percentages

To convert from a decimal to a percentage, multiply by 100 (e.g., 0.15 → 15%).
Converting from a percentage to a decimal means dividing by 100 (15% → 0.15).

Real-World Examples

Fraction of a group: 2 girls in a group of 5 children = 2/5.
Multiply by 100 → 40%.
Part of a total: 70% of 30 fruits are apples →
$(70 / 100) \times 30 = 21$
Budgeting: $12 was 30% of your total pocket money. Solve for the whole:
$\text{total} = \frac{12 \times 100}{30} = 40.$

Percentage Points

Percentage points (pp) measure the difference between two percentage values, without referring to the relative size of the change.

If someone’s polling at 10% and goes to 12%, that’s a 2 percentage point increase.
In relative terms, it’s a 20% increase (because ((12 - 10) / 10 \times 100 = 20%)).

People often say “percent” when they really mean “percentage points,” but now you’ll know the difference.

Per Mille and Basis Points

Per mille (‰) is 1/1000 or 0.1%.
Basis points (‱) are 1/10000 or 0.01%.

If you want to use a percentage calculator to handle per mille, just think of them as 10× smaller increments.

History of the Percent Sign

The modern % sign evolved from the Italian “per cento,” meaning “for a hundred.” Over time, “cento” was shortened, eventually giving us the two circles separated by a slash. Although its ancestor can be traced back to Roman times, the familiar symbol as we know it today gained popularity in the 20th century.

In programming, the percent sign often denotes the modulo operation. In physics, it can represent relative error. You may also see extra circles around the percent sign (‰, ‱) to indicate per mille or basis points.

Spelling: “Percent” or “Per Cent”?

Percent (one word) is standard in American English (“percent, dude”).
Per cent (two words) is standard in British English (“per cent, mate”).
Percentage is spelled the same way in both.

Frequently Asked Questions

What is a percentage?
A dimensionless ratio of two numbers on a scale of 0 to 100.
How do I calculate x percent of y?
1. Divide (x) by 100.
2. Multiply by (y).
How much percent of y is x?
1. Divide (x) by (y).
2. Multiply the result by 100.
How much is 60% of 1260?
60% of 1260 is 756. Here’s how:
```
60 / 100 = 0.6
0.6 × 1260 = 756
```

Conclusion

Percentages are a powerful, intuitive way to compare numbers in everyday life—be it exam scores, shopping discounts, tax rates, or statistical data. With a few formulas (and maybe a handy calculator), you can seamlessly convert between decimals, fractions, and percentages, and handle all kinds of percentage-based questions and problems.