Percentage Decrease Calculator

Decrease a number by a percentage

Initial Number

Decrease by

Other Titles

Understanding Percentage Decrease

Percentage decrease measures the reduction in a value, expressed as a percentage of the original amount. It's commonly used to calculate discounts and price reductions.

The Formula for Percentage Decrease

The calculator finds the final value after a percentage reduction.
The formula is: `Final Value = Initial Value * (1 - (Percentage / 100))`.

Calculating a percentage decrease is a two-step process. First, you determine the value of the decrease itself. Second, you subtract that value from the initial amount. The formula combines these steps for efficiency.

Breaking Down the Formula:

Core Formula

Decrease 200 by 15%
1. Decrease Amount = 200 * (15 / 100) = 200 * 0.15 = 30
2. Final Value = 200 - 30 = 170

How to Use the Calculator: A Step-by-Step Guide

Enter the number you want to decrease in the 'Initial Number' field.
Enter the percentage you want to decrease it by in the 'Decrease by' field.
Click 'Calculate' to see the final result and the amount of the reduction.

This tool simplifies the process of finding the 'after' value. It's perfect for quickly checking sale prices.

Practical Example

Scenario: A jacket is priced at $120. It's on sale for 40% off. What is the final price?
1. Enter 120 in the 'Initial Number' field.
2. Enter 40 in the 'Decrease by' field.
3. Click 'Calculate'.
4. Result: $72. The calculator also shows this was a decrease of $48.

Real-World Applications

Figuring out the final price of discounted items.
Analyzing reductions in company expenses or revenue.
Studying population declines or depreciating asset values.

Retail and Sales (Discounts):

The most common use for this calculation is shopping. A '25% off' sign means you need to calculate a 25% decrease from the original price. This calculator lets you do that instantly, so you know the exact price you'll pay at the register.

Depreciation:

Assets like cars, machinery, and electronics lose value over time. This loss is called depreciation and is often expressed as a percentage. If a car worth $30,000 depreciates by 18% in its first year, its new value is $30,000 decreased by 18%, which is $24,600.

Common Scenarios

A company reduces its marketing budget of $500,000 by 10%. The new budget is $450,000.
A city's population of 80,000 decreases by 2% in a year. The new population is 78,400.

Common Mistakes and How to Avoid Them

Calculating the decrease amount but forgetting to subtract it.
Confusing percentage decrease with percentage change.
Applying multiple discounts incorrectly.

Forgetting the Subtraction Step:

A frequent mistake is to calculate the discount amount and think that's the final price. For a $50 item with a 20% discount, the discount is $10. This is the amount saved, not the final price. You must remember to subtract it: $50 - $10 = $40.

Applying Multiple Discounts

You cannot simply add percentages together for multiple discounts. For example, 30% off followed by an additional 20% off is not 50% off. You must apply the discounts sequentially. For a $100 item: first, decrease by 30% ($100 -> $70). Then, decrease the new price by 20% ($70 -> $56). The total discount is 44%, not 50%.

Calculation Accuracy

$100 with 30% off = $70.
$70 with 20% off = $56.
Total effective discount = 44%.

Reverse Percentage Decrease

Sometimes you know the final price and the discount percentage, and need to find the original price.
The formula for this is: `Original Price = Final Price / (1 - (Percentage / 100))`.

Imagine you bought a coat for $90, and you know it was on sale for 40% off. What was the original price? You can't just add 40% to $90. You have to use the reverse formula. The 40% was taken off the unknown original price (X), so the price you paid ($90) represents 100% - 40% = 60% of the original price.

Calculation:

Finding the Original Price

A TV was bought for $600 after a 25% discount. Original price = $600 / (1 - 0.25) = $600 / 0.75 = $800.