Reverse Percentage Calculator
Free reverse percentage calculator to find original value from final value and percentage. Calculate increases, decreases, and percentage relationshipswith step-by-step solutions. Perfect for students learning percentage problems and real-world applications.
Last updated: December 15, 2024
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Reverse Percentage Result
Original Value:
100.00
Percentage Increase
Change Amount: 20.00
Formula Used:
Original = Final ÷ (1 + percentage/100)
Verification:
100.00 + 20% = 120
Step-by-Step Solution:
Reverse Percentage Tips:
- • Increase: Original = Final ÷ (1 + percentage/100)
- • Decrease: Original = Final ÷ (1 - percentage/100)
- • % Of: Original = Final ÷ (percentage/100)
- • Always verify by applying the percentage to the original
- • Use this when you know the final result and want the starting value
Reverse Percentage Types
Formula
Original = Final ÷ (1 + %/100)
Example: 120 is 20% more than what?
Formula
Original = Final ÷ (1 - %/100)
Example: 80 is 20% less than what?
Formula
Original = Final ÷ (%/100)
Example: 30 is 25% of what?
Example
$72 after 20% off = $90 original
Use decrease formula
Example
$60k after 15% raise = $52.2k original
Use increase formula
Example
90 is 75% of what = 120 original
Use percentage of formula
Quick Example Result
120 is 20% more than what number?
Original Value
100
Change Amount
20
Verification
100 + 20% = 120 ✓
How to Calculate Reverse Percentage
Reverse percentage calculations are essential for solving real-world problems where you know the final result and need to find the original value. This is common in pricing, salary negotiations, and data analysiswhere you need to work backwards from percentage changes to understand the starting point.
The Reverse Percentage Process
This systematic approach ensures accurate reverse percentage calculations for any scenario.
Reverse Percentage Formulas
The key to reverse percentage is understanding the relationship between original and final values. For increases: Final = Original × (1 + percentage/100), so Original = Final ÷ (1 + percentage/100). For decreases: Final = Original × (1 - percentage/100), so Original = Final ÷ (1 - percentage/100). For percentage of: Final = Original × (percentage/100), so Original = Final ÷ (percentage/100).
- Increase: Original = Final ÷ (1 + percentage/100)
- Decrease: Original = Final ÷ (1 - percentage/100)
- Percentage Of: Original = Final ÷ (percentage/100)
- Always verify by applying the percentage to your answer
- Check that your answer makes sense in context
Sources & References
- Basic Mathematics - Serge Lang (2nd Edition)Comprehensive coverage of percentage calculations and applications
- Pre-Algebra - Richard RusczykDetailed explanations of percentage problems and reverse calculations
- Khan Academy - Percentages and Reverse PercentagesVideo tutorials and practice problems on percentage calculations
Need help with other math topics? Check out our percentage calculator and mixed number calculator.
Get Custom Calculator for Your PlatformReverse Percentage Example
Given Values:
Final value = 120
Percentage = 20%
Operation = increase
Solution Steps:
- Step 1: Identify the given values
- Final value = 120
- Percentage = 20%
- Operation = increase
- Step 2: Set up the equation
- Final Value = Original × (1 + percentage/100)
- 120 = Original × (1 + 20/100)
- 120 = Original × 1.200
- Step 3: Solve for original value
- Original = 120 ÷ 1.200
- Original = 100.00
- Step 4: Verify the calculation
- 100.00 + 20% = 100.00 × 1.200 = 120 ✓
Final Answer:
Original Value
100
Change Amount
20
Verification
100 + 20% = 120 ✓
Price After Discount
$72 after 20% off
Original = $90
Test Score
90 is 75% of what?
Original = 120
Frequently Asked Questions
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