Percentage formulas are easiest to remember when you know what each formula is actually measuring. Most mistakes happen because the wrong base value is used, not because the formula itself is difficult.
This guide collects the percentage formulas that are most useful in SSC, Banking, Railway, and other arithmetic practice. Use it as a revision page, but make sure you understand the logic behind each formula before trying to apply it quickly.
Basic Percentage Formula
The most basic relationship is:
Percentage = (Part / Whole) × 100
For example, if 45 out of 60 students passed:
Percentage passed = 45/60 × 100 = 75%.
The important step is identifying the part and the whole correctly.
How to Find a Percentage of a Number
To find x% of a value:
x% of y = (x/100) × y
Example:
35% of 240 = 35/100 × 240 = 84.
You can also use a mental method when the percentage converts easily into a fraction. For example, 25% = 1/4.
How to Find What Percent One Number Is of Another
Use:
Percentage = (Required value / Base value) × 100
If 44 is compared with 80:
44/80 × 100 = 55%.
Always ask: “44 is what percent of which value?” The second value is usually the base.
Percentage Increase Formula
When a value increases:
Increase % = (Increase / Original value) × 100
If a salary rises from ₹20,000 to ₹23,000:
Increase = ₹3,000.
Increase % = 3,000/20,000 × 100 = 15%.
Do not divide by the new value. The percentage change is measured from the original value.
Percentage Decrease Formula
When a value decreases:
Decrease % = (Decrease / Original value) × 100
If a price falls from ₹500 to ₹425:
Decrease = ₹75.
Decrease % = 75/500 × 100 = 15%.
New Value After Percentage Increase
If a value increases by r%:
New value = Original × (100 + r)/100
Example:
A value of 800 increases by 25%.
New value = 800 × 125/100 = 1000.
You can also think of this as multiplying by 1.25.
New Value After Percentage Decrease
If a value decreases by r%:
New value = Original × (100 - r)/100
Example:
A price of ₹1,200 decreases by 20%.
New price = 1,200 × 80/100 = ₹960.
Reverse Percentage Formula
Sometimes the final value is given and the original value is missing.
If a value becomes 120% of the original:
Original = Final × 100/120
Example:
After a 20% increase, a number becomes 360.
Original = 360 × 100/120 = 300.
Formula for Successive Percentage Changes
For two successive percentage changes a% and b%, the net percentage change can be found using:
Net change = a + b + (ab/100)
Use a negative sign for a decrease.
For example, a 20% increase followed by a 20% decrease:
20 + (-20) + (20 × -20)/100 = -4%.
So the final result is a 4% decrease.
If signs feel confusing, use multipliers or assume an original value of 100. That method is often safer.
Percentage Comparison Formula
If A is compared with B:
Percentage difference relative to B = (A - B)/B × 100
Suppose A = 125 and B = 100.
A is 25% more than B.
But if you compare B with A:
(125 - 100)/125 × 100 = 20%.
So B is 20% less than A.
The percentage changes because the base changes.
Fraction to Percentage Formula
To convert a fraction into a percentage:
Fraction × 100
Examples:
- 1/2 = 50%
- 1/4 = 25%
- 3/4 = 75%
- 1/5 = 20%
- 1/8 = 12.5%
These conversions are worth remembering because they also help with mental calculation.
Percentage to Fraction
Write the percentage over 100 and simplify:
x% = x/100
Example:
35% = 35/100 = 7/20.
Percentage to Decimal
Divide the percentage by 100:
x% = x/100
Examples:
- 25% = 0.25
- 8% = 0.08
- 125% = 1.25
Common Formula Mistakes
The formulas are short, but these mistakes are common:
- Using the final value instead of the original value.
- Confusing part and whole.
- Using a percentage increase formula for a direct percentage question.
- Adding successive percentage changes without checking the base.
- Ignoring the direction of comparison.
- Rounding too early.
For a deeper review, use Common Percentage Mistakes in Exams.
Worked Formula Examples
The examples below show how to choose the formula before doing the calculation.
Example 1: Find the Percentage
54 out of 90 students passed.
54/90 × 100 = 60%.
Example 2: Percentage Increase
A value increases from 400 to 460.
Increase = 60.
60/400 × 100 = 15%.
Example 3: Reverse Percentage
After a 25% increase, a number becomes 625.
Original = 625 × 100/125 = 500.
Example 4: Successive Change
A value increases by 10% and then by 20%.
Net change = 10 + 20 + (10 × 20)/100 = 32% increase.
Quick Practice
- What percent of 80 is 44?
- Find the decrease percentage from 500 to 425.
- After a 20% increase, a number becomes 720. Find the original number.
- A value rises by 10% and then falls by 10%. Find the net change.
- Convert 37.5% into a fraction.
How to Revise Percentage Formulas
Do not try to memorise this page word for word. Keep a small formula sheet with the basic percentage, percentage change, new value, reverse percentage, and successive-change formulas.
Then solve a few questions using each formula. Formula recall becomes much stronger when it is linked to a question pattern.
Continue Your Percentage Study
Return to the Percentage Master Guide for the full learning path.
For faster calculation methods, use Percentage Tricks for Fast Calculation. For word-based questions, continue with Percentage Word Problems Explained.
When you are ready to practise, move to Percentage Practice Set 1.