How to Calculate Percentage

Percentages appear in discounts, taxes, exam scores, salary hikes, and investment returns. Here is the complete guide — formulas, worked examples, and common mistakes — so you can calculate any percentage with confidence.

What is a percentage?

A percentage is a number expressed as a fraction of 100. The word comes from the Latin per centum, meaning "by the hundred." When you say 45%, you mean 45 out of every 100 — or equivalently, the fraction 45/100 = 0.45.

Percentages are useful because they give a standard scale for comparison. A score of 72 out of 90 and a score of 80 out of 100 are hard to compare directly — but converting both to percentages (80% vs 80%) immediately shows they are equal.

The basic percentage formula

There are three core calculations, all based on the same relationship:

Percentage = (Part ÷ Whole) × 100
Part       = (Percentage × Whole) ÷ 100
Whole      = (Part ÷ Percentage) × 100

Each formula is a rearrangement of the same equation. Once you know any two of the three values, you can find the third.

Example: What is 30% of 250?

Part = (30 × 250) ÷ 100
     = 7500 ÷ 100
     = 75

Answer: 30% of 250 is 75.

Example: 45 is what percent of 180?

Percentage = (45 ÷ 180) × 100
           = 0.25 × 100
           = 25%

Answer: 45 is 25% of 180.

Skip the arithmetic — enter any two values and get the answer instantly.

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Percentage increase and decrease

Percentage change measures how much a value has grown or shrunk relative to its original amount.

% Change = ((New Value − Old Value) ÷ Old Value) × 100

A positive result means an increase (e.g. price went up, sales grew).
A negative result means a decrease (e.g. price was reduced, weight lost).

Example: Salary increased from ₹40,000 to ₹46,000

% Increase = ((46000 − 40000) ÷ 40000) × 100
           = (6000 ÷ 40000) × 100
           = 15%

Answer: The salary increased by 15%.

Example: Product price dropped from ₹1,200 to ₹900

% Decrease = ((900 − 1200) ÷ 1200) × 100
           = (−300 ÷ 1200) × 100
           = −25%

Answer: The price decreased by 25%.

Reverse percentage — find the original value

Sometimes you know the final value after a percentage was applied, and you want to work backwards to find the original. This is called a reverse percentage.

Original = Final Value ÷ (1 + percentage÷100)   [if percentage was added]
Original = Final Value ÷ (1 − percentage÷100)   [if percentage was subtracted]

Example: A product costs ₹590 after 18% GST. What was the base price?

Original = 590 ÷ (1 + 18÷100)
         = 590 ÷ 1.18
         = ₹500

Answer: The base price before tax was ₹500.

Example: A shirt costs ₹680 after a 15% discount. What was the original price?

Original = 680 ÷ (1 − 15÷100)
         = 680 ÷ 0.85
         = ₹800

Answer: The original price was ₹800.

Adding and subtracting a percentage

To add a percentage to a number (e.g. apply a surcharge or markup):

Result = Number × (1 + percentage÷100)

To subtract a percentage from a number (e.g. apply a discount):

Result = Number × (1 − percentage÷100)

Example: Add 12% GST to ₹2,500

Result = 2500 × (1 + 12÷100)
       = 2500 × 1.12
       = ₹2,800

Example: Apply a 20% discount on ₹1,500

Result = 1500 × (1 − 20÷100)
       = 1500 × 0.80
       = ₹1,200

Common mistakes

Calculating percentage on the wrong base. Always apply the percentage to the original (pre-change) value. Applying a 10% increase and then a 10% decrease does not bring you back to the start — it leaves you at 99% of the original.
Confusing percentage points with percentages. If interest rates rise from 4% to 6%, that is a 2 percentage-point increase, but a 50% increase in the rate itself. These are different things.
Reversing percentages incorrectly. To find the original price before a 20% markup, do not subtract 20% from the marked-up price. Instead, divide by 1.20. Subtracting 20% from ₹120 gives ₹96, not ₹100.
Rounding too early. When chaining multiple percentage calculations, round only at the final step to avoid compounding errors.
Treating percentage decrease and increase as symmetrical. A 50% decrease followed by a 50% increase does not restore the original value — you end up at 75%.

Use the calculator to verify your answers or work through any percentage problem step by step.

Try the Percentage Calculator

Also try

Discount Calculator — find sale price, savings amount, and effective discount %
GST Calculator — add or remove 5%, 12%, 18%, or 28% GST instantly
EMI / Loan Calculator — break down your loan into monthly instalments
SIP Calculator — project returns on monthly mutual fund investments

FAQ

What is the formula for percentage?

The basic formula is: Percentage = (Part ÷ Whole) × 100. To find the part: Part = (Percentage × Whole) ÷ 100. To find the whole: Whole = (Part ÷ Percentage) × 100.

How do I calculate percentage increase?

Use the formula: % Increase = ((New Value − Old Value) ÷ Old Value) × 100. For example, if a price rises from ₹500 to ₹600, the increase is ((600 − 500) ÷ 500) × 100 = 20%.

How do I find the original price before a discount?

Divide the discounted price by (1 − discount÷100). Example: if an item costs ₹400 after a 20% discount, the original price = 400 ÷ 0.80 = ₹500. Do not add 20% back — that gives the wrong answer.

Is a 10% increase followed by a 10% decrease the same as no change?

No. If you increase ₹100 by 10%, you get ₹110. Then decreasing ₹110 by 10% gives ₹99 — a net loss of 1%. Percentage increases and decreases are not symmetrical because they apply to different base values.

How do I calculate percentage in Excel or Sheets?

For "X% of Y": type =A1*B1/100 or simply =A1*B1%. For percentage change: =(B1-A1)/A1 then format the cell as a percentage. Most spreadsheet apps handle percentage formatting automatically.