Percentage Calculator

🧮 What Is a Percentage?

A percentage is a mathematical way to express a number as a fraction of 100. It’s a simple way to compare one value to another without using complex ratios or fractions. The term “percent” comes from the Latin per centum, meaning “by the hundred.”

Percentages are written with the symbol % or sometimes with the words percent or pct.
For example:

• 25% means 25 out of every 100.

• 50% is equal to 0.5 in decimal form or ½ as a fraction.

In short, percentages show “how much of something” in an easy-to-understand way.

📘 How to Calculate Percentage

The general percentage formula is:

P×V1=V2P × V₁ = V₂P×V1​=V2​

Where:

• P = Percentage (in decimal form)

• V₁ = Original or base value

• V₂ = Result after applying the percentage

To find the percentage, rearrange the formula:

P=V2V1×100P = \frac{V₂}{V₁} × 100P=V1​V2​​×100

Example:
If 25 out of 50 students are male:

2550×100=50\frac{25}{50} × 100 = 50%5025​×100=50

So, 50% of the students are male.

Another example:

P×30=1.5⇒P=1.530=0.05×100=5P × 30 = 1.5 \Rightarrow P = \frac{1.5}{30} = 0.05 × 100 = 5%P×30=1.5⇒P=301.5​=0.05×100=5

That means 5% of 30 is 1.5.

⚙️ Percentage Difference Formula

The percentage difference tells you how much two numbers differ relative to their average value.
It’s useful when comparing prices, measurements, or data changes.

Percentage Difference=∣V1−V2∣(V1+V2)/2×100\text{Percentage Difference} = \frac{|V₁ – V₂|}{(V₁ + V₂)/2} × 100Percentage Difference=(V1​+V2​)/2∣V1​−V2​∣​×100

Example:
If one value is 10 and the other is 6:

∣10−6∣(10+6)/2=48=0.5=50\frac{|10 – 6|}{(10 + 6)/2} = \frac{4}{8} = 0.5 = 50%(10+6)/2∣10−6∣​=84​=0.5=50

So, the difference between 10 and 6 is 50%.

📈 Percentage Change Formula

The percentage change shows how much a value has increased or decreased compared to its starting point.
It’s calculated using:

Percentage Change=(New Value−Old Value)Old Value×100\text{Percentage Change} = \frac{(\text{New Value} – \text{Old Value})}{\text{Old Value}} × 100Percentage Change=Old Value(New Value−Old Value)​×100

• If the result is positive, it’s a percentage increase.

• If it’s negative, it’s a percentage decrease.

Example:

• Increase: 500 increased by 10% →
  $500\times (1+0.1)=550$

• Decrease: 500 decreased by 10% →
  $500\times (1-0.1)=450$

So, a 10% increase of 500 gives 550, and a 10% decrease gives 450.

💡 Key Takeaways

• Percentages are an easy way to compare values as parts of 100.

• Use the formula P × V₁ = V₂ to find the missing value.

• The percentage difference shows how two values compare on average.

• The percentage change tracks growth or reduction over time.

If you don’t want to calculate manually, try the free online Percentage Calculator — it instantly gives you accurate results for increase, decrease, and difference calculations.