Percent Off Formula
Find how much of a discount was applied by comparing the original and sale prices.
Percent Off = (Original − Sale) / Original × 100
Sale Price Formula
Given the original price and discount percentage, find the final sale price.
Sale = Original × (1 − %Off/100)
Original Price Formula
Work backward from the sale price and discount to find what the item originally cost.
Original = Sale / (1 − %Off/100)
How It Works
A percent-off sale reduces the original price by a given percentage. This calculator lets you find the discount percentage, the sale price, or the original price when you know the other two values. It handles the simple formula: Sale = Original × (1 − %Off/100).
Example Problem
A $120 jacket is on sale for $84. What is the percent off?
- Identify the known values: Original Price = $120, Sale Price = $84
- Calculate the discount amount: $120 − $84 = $36
- Divide the discount by the original price: $36 / $120 = 0.30
- Multiply by 100 to convert to a percentage: 0.30 × 100 = 30
- Add the percent symbol: 30%
- Verify: $120 × (1 − 30/100) = $120 × 0.70 = $84 ✓
When to Use Each Variable
- Solve for Percent Off — when you know the original and sale prices and want to find the discount percentage, e.g., comparing deals across stores.
- Solve for Sale Price — when you know the original price and discount percentage, e.g., calculating what you will pay at checkout.
- Solve for Original Price — when you know the sale price and discount percentage, e.g., finding what an item cost before a clearance markdown.
Key Concepts
A percent-off discount reduces the original price by a fixed percentage. The sale price equals the original price multiplied by (1 minus the discount rate). Stacked discounts do not add — a 20% off followed by 10% off yields 28% total, not 30%, because the second discount applies to the already-reduced price.
Applications
- Retail shopping: quickly calculating the final price during sales and clearance events
- Price comparison: converting different discount offers to the same percentage for fair comparison
- Retail management: setting markdown percentages to hit target sale prices during promotions
- Budgeting: estimating savings from coupons and promotional codes before purchasing
Common Mistakes
- Adding stacked discounts — a 20% off plus 10% off is not 30% off; the second discount applies to the reduced price, yielding 28% total
- Calculating the original price by adding the discount percentage to the sale price — you must divide by (1 − discount/100), not add the percentage
- Applying the discount to the wrong base — percent off is always relative to the original price, not the sale price or a previous discount
Frequently Asked Questions
How do I figure out the sale price after a percentage discount?
Multiply the original price by (1 minus the discount divided by 100). For example, a 30% discount on a $120 item: $120 × (1 − 30/100) = $120 × 0.70 = $84 sale price.
What is the difference between percent off and percent change?
Percent off measures the discount from the original price to the sale price and is always positive. Percent change measures the relative difference between any two values and can be positive (increase) or negative (decrease). A 25% off sale and a −25% price change describe the same reduction, but percent change applies to any direction.
How do I calculate 20 percent off a price?
Multiply the original price by 0.20 to get the savings, then subtract from the original. For a $50 item: $50 × 0.20 = $10 off, so you pay $40. Equivalently, multiply by 0.80 directly: $50 × 0.80 = $40.
Do stacked discounts add up?
No. A 20% discount followed by an additional 10% off is not 30% total. The second discount applies to the already-reduced price: $100 → $80 → $72, which is 28% off overall.
How do I find the original price from a sale price?
Divide the sale price by (1 − discount/100). If an item is $60 after a 25% discount: $60 / 0.75 = $80 original price.
Is a bigger percent off always a better deal?
Not necessarily. A 50% off a $30 item saves you $15, while 20% off a $200 item saves $40. The total dollar savings and the item value both matter. Compare the final sale price or dollar amount saved, not just the percentage.
How do I calculate percent off for a buy-one-get-one deal?
For a true BOGO (buy one, get one free), you pay for one item and get two. The effective discount is 50% off the combined total. For BOGO 50% off, you pay 1.5× the single price for two items, which is 25% off the combined total.
Percent Off Formula
The percent-off formula calculates the sale price after applying a percentage discount to the original price:
Sale Price = Original Price × (1 − Discount / 100)
Where:
- Sale Price — the final price you pay after the discount
- Original Price — the full retail price before any discount
- Discount — the percentage taken off, expressed as a whole number (e.g., 25 for 25%)
You can rearrange this formula to solve for any variable. To find the percent off, use: Percent Off = (Original − Sale) / Original × 100. To find the original price, use: Original = Sale / (1 − Discount/100).
Worked Examples
Retail Shopping
How much do you save on a Black Friday TV deal?
A 65-inch TV originally priced at $1,200 is marked 35% off for Black Friday. What is the sale price and how much do you save?
- Discount amount: $1,200 × 35/100 = $420
- Sale Price = $1,200 × (1 − 35/100) = $1,200 × 0.65
- Sale Price = $780
You save $420. Remember that sales tax applies to the discounted price, not the original — so your total at checkout is $780 plus tax.
Business Pricing
What wholesale markdown moves stale inventory?
A retailer needs to sell winter jackets originally priced at $250. They set the clearance price at $100. What percent markdown did they apply?
- Discount amount: $250 − $100 = $150
- Percent Off = ($150 / $250) × 100
- Percent Off = 60%
A 60% markdown is aggressive but common for end-of-season clearance. The retailer recovers some cost and frees up shelf space for new inventory.
Real Estate
What was the original asking price before a negotiated reduction?
A home sold for $425,000 after the seller accepted a 15% price reduction. What was the original listing price?
- Original = Sale / (1 − Discount/100)
- Original = $425,000 / (1 − 15/100) = $425,000 / 0.85
- Original Price = $500,000
The seller reduced the listing by $75,000. In competitive markets, price reductions of 5-15% are typical when homes sit on the market longer than expected.
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