Reverse Percentage Calculator

Find the original value before a percentage increase, decrease, or when given a percentage of the original

Calculate Original Value

Calculation Type

Final Value (F)

Percentage (P)

Find the original when you know a percentage of it equals the final value

Enter the final value and percentage to calculate the original value

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How to Use This Calculator

Step-by-step guide to get accurate results

What is a Reverse Percentage Calculator?

A reverse percentage calculator is an essential tool in finance, retail, and accounting that allows users to determine the original value of a number before a percentage change was applied. Unlike a standard percentage calculator, which calculates the percentage of a number, reverse percentage calculations work backward to identify the base value. Free reverse percentage calculator online options allow quick calculations without installing software, and reverse percentage calculator Excel formulas make it easy to handle multiple data points in a spreadsheet.

How the Calculator Works

The Reverse Percentages Calculator works backwards from a final value and a percentage to find the original number before the percentage was applied. This is also called a reverse percentage or inverse percentage calculation.

Type 1: Percentage of Original

You know a percentage of a number and the result, and want the original number. Example: 32% of a number is 150 — what is the number?

Type 2: After Increase or Decrease

You know a final value after a percentage increase or decrease and want the original value. Example: After a 12% decrease, the price is $15,000 — what was the original price?

Reverse Percentage Calculator Formula

The reverse percentage formula is simple:

\text{Original Value} = \frac{\text{Final Value}}{1 \pm \frac{\text{Percentage Change}}{100}}

Use + for percentage increase and - for percentage decrease.

Formula Reference Table

Final Value	Percentage Change	Type	Original Value
$120</td><td>20%</td><td>Increase</td><td>$ 100
$80</td><td>20%</td><td>Decrease</td><td>$ 100
$150</td><td>50%</td><td>Increase</td><td>$ 100
$75</td><td>25%</td><td>Decrease</td><td>$ 100

Three Main Calculation Cases

Case A: Given Percentage of Original

When you know that a final number is P% of the original number:

O = \frac{F}{(P/100)}

So you divide by the percentage expressed as a decimal. Example: 70% of a number = 210. Solution:

O = 210 \div (70/100) = 210 \div 0.70 = 300

Original number = 300

Case B: Reverse After Percentage Increase

If the final value includes a percentage increase (e.g., +P%):

O = \frac{F}{1 + (P/100)}

Explanation: final = original × (1 + P/100) → solve for original. Example: Final value 320 which is 15% more than original.

O = \frac{320}{1 + 0.15} = \frac{320}{1.15} \approx 278.26

Original ≈ 278.26

Case C: Reverse After Percentage Decrease

If the final value is after a percentage decrease (e.g., −P%):

O = \frac{F}{1 - (P/100)}

Explanation: final = original × (1 − P/100) → solve for original. Example: After a 20% decrease the price is

40,000.

O = \frac{40,000}{1 - 0.20} = \frac{40,000}{0.80} = 50,000

Original price =

50,000

Step-by-Step Method

Follow these steps to calculate reverse percentages:

Step 1: Identify the Type

Determine if the change was an increase (final value is more than original), decrease (final value is less than original), or percentage of original.

Step 2: Convert to Decimal

Convert the percentage to a decimal by dividing by 100. Example: 25% → 0.25

Step 3: Apply the Formula

Use the appropriate formula: For increase → divide by (1 + decimal), For decrease → divide by (1 - decimal), For % of original → divide by (P/100)

Step 4: Calculate

Perform the division to find the original value. This gives you the value before the percentage change.

Practical Examples

Example 1: Reverse Increase

Problem: Final value = 150 after a 20% increase. Solution:

O = \frac{150}{1 + 0.2} = \frac{150}{1.2} = 125

Original value = 125. Verification: 125 + (125 × 0.2) = 125 + 25 = 150 ✓

Example 2: Reverse Decrease

Problem: Final value = 80 after a 20% decrease. Solution:

O = \frac{80}{1 - 0.2} = \frac{80}{0.8} = 100

Original value = 100. Verification: 100 - (100 × 0.2) = 100 - 20 = 80 ✓

Example 3: Percentage of Original

Problem: 32% of a number is 150. Solution:

O = \frac{150}{0.32} = 468.75

Original value = 468.75. Verification: 468.75 × 0.32 = 150 ✓

Types of Reverse Percentage Calculations

Reverse Percentage Discount Calculator: Finds original price before a discount
Reverse Percentage Increase Calculator: Determines initial value before a price hike
Reverse Percentage Decrease Calculator: Determines initial value before a reduction
Reverse Percentage Tax Calculator: Calculates pre-tax amount from the final price

Common Scenarios Table

Scenario	Formula	Use Case
Discount	Original = Final ÷ (1 − %Discount/100)	Sales, shopping
Price Increase	Original = Final ÷ (1 + %Increase/100)	Markups, inflation
Tax Calculation	Original = Final ÷ (1 + %Tax/100)	VAT, GST, sales tax
Reverse Percentage Change	Original = Final ÷ (1 ± %Change/100)	Financial analysis

When Reverse Percentages Are Useful

Reverse percentage calculations are used in various real-world scenarios:

Retail and Shopping

Finding original price before a discount or sale. Example: A shirt costs

24 after a 40% discount. What was the original price? Solution:

24 ÷ (1 - 0.40) =

24 ÷ 0.60 =

Tax Calculations

Finding pre-tax amounts when you know the total including tax. Example: Total with 10% tax is

110. What was the pre-tax amount? Solution:

110 ÷ (1 + 0.10) =

110 ÷ 1.10 =

100

Salary and Pay

Undoing pay raises or reductions to find the original salary. Backtracking original values in financial data analysis.

Business and Finance

Calculating original investment amounts, understanding price changes, analyzing percentage-based growth or decline in metrics.

Online vs Excel vs Manual Methods

Online Tools

Quick, free, and convenient. Search for 'reverse percentages calculator online' or 'free reverse percentage calculator'. Ideal for one-off calculations and quick checks.

Excel Method

Perfect for bulk calculations, reports, and automated workflows. For increase: =FinalValue/(1+Percentage/100). For decrease: =FinalValue/(1-Percentage/100). Great for handling multiple data points simultaneously.

Manual Method

Best for learning, small calculations, or when a calculator is not available (reverse percentages without a calculator). Helps understand the underlying mathematical principles.

Common Mistakes to Avoid

Using the wrong formula: Make sure to use + for increases and - for decreases
Not converting percentages: Always convert percentage to decimal (divide by 100)
Dividing by percentage instead of multiplier: Remember to use (1 ± P/100), not just P/100
Rounding too early: Keep precision during calculation, round only the final answer

Frequently Asked Questions

How do I calculate reverse percentages?

Use the formula: Original Value = Final Value ÷ (1 ± Percentage Change/100). Add the percentage for increases, subtract for decreases. For example, if a value is

120 after a 20% increase, the original is

120 ÷ 1.20 = $100.

Can I calculate reverse percentages without a calculator?

Yes, divide the final value by 1 plus or minus the decimal equivalent of the percentage. For mental math, convert the percentage to a simple fraction when possible.

Is there a reverse percentage Excel formula?

Yes, for an increase: =FinalValue/(1+Percentage/100); for a decrease: =FinalValue/(1-Percentage/100). For percentage of: =FinalValue/(Percentage/100).

What is the difference between reverse percentage and percentage change?

Reverse percentage finds the original value before a change; percentage change calculates the difference from the original to final value as a percentage.

How do I find the original price after a discount?

Use the formula: Original Price = Sale Price ÷ (1 - Discount%/100). For example, if an item costs

60 after a 25% discount:

60 ÷ (1 - 0.25) =

60 ÷ 0.75 =

80.

Can reverse percentage calculations give negative results?

The original value should always be positive if your inputs are correct. A negative result indicates an error in the calculation type or that the decrease percentage is 100% or more.

How accurate are reverse percentage calculators?

Reverse percentage calculators are mathematically exact. Any rounding is typically done only in the final display, maintaining precision throughout the calculation.

What if I need to reverse multiple percentage changes?

Apply each reverse calculation in reverse order. If a value went through +10% then -5%, reverse the -5% first, then reverse the +10%.

Are there free reverse percentage calculators online?

Yes, many websites offer free reverse percentage calculators, including tools for discounts, taxes, and increases. Our calculator is completely free and requires no registration.

Why is my answer different from the forward calculation?

Due to compounding effects. A 50% increase followed by a 50% decrease does not return to the original value because the percentages are applied to different base numbers.

Final Value	Percentage Change	Type	Original Value
$120</td><td>20%</td><td>Increase</td><td>$ 100
$80</td><td>20%</td><td>Decrease</td><td>$ 100
$150</td><td>50%</td><td>Increase</td><td>$ 100
$75</td><td>25%</td><td>Decrease</td><td>$ 100

Final Value

Percentage Change

Type

Original Value

120</td><td>20%</td><td>Increase</td><td>

100

80</td><td>20%</td><td>Decrease</td><td>

100

150</td><td>50%</td><td>Increase</td><td>

100

75</td><td>25%</td><td>Decrease</td><td>

100

Scenario

Formula

Use Case

Discount

Original = Final ÷ (1 − %Discount/100)

Sales, shopping

Price Increase

Original = Final ÷ (1 + %Increase/100)

Markups, inflation

Tax Calculation

Original = Final ÷ (1 + %Tax/100)

VAT, GST, sales tax

Reverse Percentage Change

Original = Final ÷ (1 ± %Change/100)

Financial analysis