Percentage Formula Explained with Examples (India)

Behind every “20% off,” “18% GST,” and “8.5% home loan” lies a single, elegant formula. Once you understand how that formula is built and how to rearrange it, you can solve any percentage problem — not just plug numbers into a percentage calculator and hope. This guide explains the percentage formula from first principles, with worked Indian examples in rupees and marks.

Key takeaway: There is really only one percentage formula. The three “different” formulas people memorise are just that one equation solved for a different unknown.

The Master Percentage Formula

A percentage expresses a part as a share of a whole, scaled to 100. The master formula is therefore:

Percentage (%) = (Part ÷ Whole) × 100

Here, the “Part” is the quantity you are measuring and the “Whole” is the total it belongs to. Multiplying by 100 rescales the fraction so that the whole always equals 100. Everything else in percentages flows from rearranging this one equation.

The Fraction–Decimal–Percentage Triangle

A percentage, a decimal and a fraction are three ways of writing the same value. 50% = 0.5 = 1/2; 25% = 0.25 = 1/4; 18% = 0.18 = 18/100. To convert a percentage to a decimal, divide by 100; to convert a decimal to a percentage, multiply by 100. This flexibility is what makes the formula so powerful — you can slide between forms to make a calculation easier. For example, finding 25% of a bill is often faster as “a quarter of” than as “0.25 times.”

Rearranging the Formula: Three Practical Forms

Depending on which quantity is missing, the master formula takes one of three shapes:

Worked Example 1: Finding the Part (GST)

A phone costs ₹30,000 before tax at 18% GST. The tax (the part) is (30000 × 18) ÷ 100 = ₹5,400. Final price ₹35,400. This is the first form — total and rate known, part unknown.

Worked Example 2: Finding the Total (Reverse GST)

You paid ₹5,400 as 18% GST and want to know the pre-tax price. Total = (5400 × 100) ÷ 18 = ₹30,000. This reverse form is essential when an invoice shows only the tax amount, or when you must extract the base price from a GST-inclusive MRP.

Worked Example 3: Finding the Rate (Marks)

A student scored 612 out of 720 in a competitive exam. The rate is (612 ÷ 720) × 100 = 85%. This third form answers “what percentage did I get?”

The Percentage-Change Formula

To measure growth or decline, use Change % = ((New − Old) ÷ Old) × 100. If petrol rises from ₹100 to ₹106 per litre, the increase is ((106 − 100) ÷ 100) × 100 = 6%. The critical rule is that the denominator is always the original value. Divide by the new value and your answer will be wrong — a mistake that quietly distorts many household budget calculations.

Successive Percentages: Why They Don’t Add

A common trap is assuming a 20% discount followed by 18% GST cancels to a net “2% off.” They don’t, because each percentage applies to a different base. On a ₹1,000 item: after 20% discount the price is ₹800; 18% GST on ₹800 adds ₹144, giving ₹944. The effective change from ₹1,000 is a 5.6% reduction, not 2%. Successive percentages combine multiplicatively, not additively — a fact that matters for stacked festival offers and for compound interest.

Benefits of Understanding the Formula

Understanding the formula rather than memorising isolated tricks means you never freeze when a problem is worded differently. You can extract a base price from a tax-inclusive MRP, check whether a “flat 15% cashback” is calculated before or after GST, and verify your salary’s revised figure after a percentage hike. For competitive-exam aspirants, a firm grip on rearrangement turns profit-and-loss and data-interpretation questions — heavily weighted in SSC, banking and CAT — into quick mental maths rather than guesswork.

Challenges and Limitations

The formula itself is simple, but real problems hide the “whole.” Reverse-percentage questions trip people up because it is tempting to add back the same percentage you removed, which does not restore the original. Successive percentages and percentages-of-percentages require care about which base applies at each step. And because Indian tax invoices often round each line item, a formula-perfect answer can differ from a printed total by a rupee or two — correct in method, off only in rounding convention.

Common Mistakes to Avoid

• Adding successive percentages. A 10% rise then a 10% fall does not return you to the start; it leaves you 1% lower.
• Reversing a percentage by re-adding it. To undo a 20% discount you divide by 0.8, you do not add 20% back.
• Using the new value as the base. Percentage change always divides by the original value.
• Mixing up part and whole. Putting the total on top and the part on the bottom flips the answer.
• Forgetting the ×100. Stopping at the decimal reports 0.85 instead of 85%.
• Ignoring the GST base. GST is charged on the discounted price, so applying it to the MRP overstates the tax.

Best Practices and Expert Recommendations

• Label every quantity. Write “Part =”, “Whole =”, “Rate =” before solving so you pick the right rearrangement.
• Convert to decimals for multiplication. 0.18 × amount is faster and cleaner than (18/100) × amount.
• Treat successive percentages as multipliers. A 20% discount is ×0.80; 18% GST is ×1.18. Chain the multipliers.
• Keep the original value as the base for change. Never divide by the new figure.
• Round once, at the end. Carrying full decimals avoids compounding rounding errors across steps.
• Cross-check with a tool. For money and marks, confirm your rearranged answer using a simple percentage tool before you rely on it.

Expert insight: Memorising three formulas is harder than understanding one. Learn the master equation and how to solve it for each unknown, and you will never confuse the “find the part” case with the “find the total” case again.

The percentage formula is one of the highest-return pieces of maths you can master for Indian financial and academic life. Understand how it is built, practise rearranging it, and verify important results — the mechanics you have learned here work identically whether the numbers are marks, rupees, or interest rates.

Two More Useful Percentage Formulas

Beyond the three core rearrangements, two related formulas appear often in Indian academic and financial life. The first is percentage error, used in science labs and measurement: Percentage Error = (|Measured − Actual| ÷ Actual) × 100. A student who measures a rod as 9.8 cm when it is actually 10 cm has an error of (0.2 ÷ 10) × 100 = 2%. This formula is standard in CBSE and state-board physics practicals, and understanding it is really just the percentage-change formula applied to accuracy.

The second is the distinction between a percentage and a percentage point, which matters enormously in finance. When the RBI changes the repo rate from 6.5% to 6.75%, that is a rise of 0.25 percentage points, not a 0.25% rise. In relative terms it is actually a 3.8% increase. News reports and loan discussions constantly blur these two, and getting them right protects you from misreading how much your EMI or FD return will actually change.

Quick Formula Recap

• Find the part: Part = (Total × Rate) ÷ 100.
• Find the total: Total = (Part × 100) ÷ Rate.
• Find the rate: Rate = (Part ÷ Total) × 100.
• Percentage change: ((New − Old) ÷ Old) × 100.
• Percentage error: (|Measured − Actual| ÷ Actual) × 100.

Keeping these five on a single index card covers virtually every percentage question you will meet in Indian schoolwork, competitive exams, and everyday money decisions. Once the pattern is familiar, you will recognise which one a problem needs within seconds, and you can always confirm the arithmetic with a calculator before you rely on the answer.

FAQs

What is the basic percentage formula?
The basic formula is Percentage = (Part ÷ Whole) × 100. Rearranged, it finds the part (Total × % ÷ 100) or the total (Part × 100 ÷ %) when those are the unknowns.

How do I reverse a percentage to find the original amount?
Divide the known part by the rate expressed as a decimal. If ₹5,400 is 18% GST, the base price is 5400 ÷ 0.18 = ₹30,000. To undo a 20% discount, divide the paid price by 0.80.

Why can’t I just add successive percentages?
Because each percentage applies to a different base. Combine them as multipliers instead — a 20% discount then 18% GST is ×0.80 ×1.18, giving a net multiplier of 0.944, or a 5.6% reduction.

What is the percentage-change formula?
Change % = ((New − Old) ÷ Old) × 100. The denominator is always the original value; a negative result indicates a decrease.

How are percentages, fractions and decimals related?
They are three forms of the same value. Divide a percentage by 100 to get a decimal, and write that over 100 to get a fraction — 25% = 0.25 = 1/4.