Discount Calculator

At its most basic, a discount is just a reduction from the original price. The math is straightforward once you know what you're solving for.

The most common situation: you know the original price and the discount percentage, and you want to know how much money you're saving. Here's how that works:

1. Convert the discount percentage to a decimal by dividing by 100. So 25% becomes 0.25.
2. Multiply that decimal by the original price. That gives you the discount amount.
3. Subtract the discount amount from the original price to get the sale price.

Example: an item costs $80 and it's 25% off. Multiply 80 × 0.25 = $20 savings. Subtract: $80 − $20 = $60 sale price.

Simple enough, but the variations (finding the percentage, finding the original price, stacking multiple discounts) each need their own approach. The sections below cover all of them.

Sometimes you already know the original price and the sale price, and you want to figure out what percentage off that actually represents. Retailers don't always make this obvious.

The formula is:

Discount % = ((Original Price − Sale Price) ÷ Original Price) × 100

Walk through it step by step:

1. Subtract the sale price from the original price to get the dollar amount saved.
2. Divide that savings amount by the original price.
3. Multiply by 100 to convert to a percentage.

Example: a jacket was $120 and is now selling for $78. The difference is $42. Divide: 42 ÷ 120 = 0.35. Multiply by 100: 35% off.

This is especially handy when you're comparing two different sales across stores. A $30 discount on a $60 item (50% off) beats a $30 discount on a $200 item (15% off) in percentage terms, even though the dollar savings look identical.

The sale price is what you actually pay after the discount is applied. There are two clean ways to calculate it depending on what feels more intuitive to you.

Method 1 (subtract the discount):
Sale Price = Original Price − (Original Price × Discount % ÷ 100)

Method 2 (multiply by the remainder):
Sale Price = Original Price × (1 − Discount % ÷ 100)

Method 2 is faster once you get used to it. If something is 30% off, you're paying 70% of the original price. Multiply the original price by 0.70 and you're done in one step.

• 20% off → multiply by 0.80
• 35% off → multiply by 0.65
• 50% off → multiply by 0.50
• 75% off → multiply by 0.25

Example: a $250 TV is 35% off. Multiply 250 × 0.65 = $162.50. That's your checkout price before tax.

This one trips people up. You see a sale tag showing the current price and the percentage off, but you want to know what the item originally sold for. Maybe you're checking whether a store inflated the price before marking it down.

The formula:

Original Price = Sale Price ÷ (1 − Discount % ÷ 100)

Why does this work? If an item is 40% off, the sale price represents 60% of the original. Dividing by 0.60 scales it back up to 100%.

Example: you see a pair of shoes on sale for $90, marked 40% off. Divide: 90 ÷ 0.60 = $150 original price.

A quick sanity check: take that $150, find 40% of it (150 × 0.40 = $60), subtract from $150, and you get $90. Matches. You're good.

This formula is also useful when a cashier applies a discount at checkout and you want to reverse-engineer the shelf price from your receipt.

Stacked discounts don't add together the way most people assume. A 20% off coupon on top of a 30% off sale is not 50% off. The discounts apply sequentially, each one calculated on the price after the previous discount was taken.

Here's how to handle it:

1. Apply the first discount to the original price.
2. Take the result and apply the second discount to that number.
3. Repeat for any additional discounts.

Example: an item is $200. Store sale is 30% off, plus you have a 20% off coupon.

• After 30% off: $200 × 0.70 = $140
• After 20% off: $140 × 0.80 = $112

Total savings: $88. That's an effective discount of 44%, not 50%.

To find the effective combined discount percentage from two stacked discounts, use this:

Effective Discount % = 100 − ((1 − D1/100) × (1 − D2/100) × 100)

For 30% and 20%: 100 − (0.70 × 0.80 × 100) = 100 − 56 = 44% effective discount.

Order doesn't matter for the final price. Whether the store applies the 30% first or the 20% first, you end up at $112 either way.

Here's a consolidated reference for all the key formulas covered in this guide. Useful to keep handy when you need to switch between different unknowns.

For quick mental math, the "1 minus" shortcut is your best friend. Instead of finding the discount and subtracting, just multiply the original price by what percentage you're actually paying. 15% off means you pay 85%, so multiply by 0.85. It cuts out a step and reduces errors.

If you're working with a calculator or spreadsheet, these formulas translate directly. In Excel or Google Sheets, a formula like =B2*(1-C2) where B2 is the original price and C2 is the discount as a decimal will spit out the sale price instantly.

Sometimes seeing the math applied to realistic scenarios makes it click faster than any formula explanation. Here are several worked examples covering different situations.

Example 1: Basic percentage off
A $45 shirt is 20% off. Sale price = 45 × 0.80 = $36. You save $9.

Example 2: Finding the discount percentage
A laptop was $899 and is now $674.25. Savings = $224.75. Discount % = (224.75 ÷ 899) × 100 = 25% off.

Example 3: Finding the original price
A handbag is on sale for $168, listed as 30% off. Original price = 168 ÷ 0.70 = $240.

Example 4: Stacked discounts
Furniture is 25% off, and you have an additional 10% off coupon. Original price: $600.
After 25%: 600 × 0.75 = $450. After 10%: 450 × 0.90 = $405. You save $195 total (32.5% effective discount).

Example 5: Comparing two deals
Store A sells a $300 item for $210 (30% off). Store B sells the same item for $225 with a $30 mail-in rebate, ending at $195. Store B's effective discount: (105 ÷ 300) × 100 = 35% off. Store B wins, but only if you actually send in the rebate.

Not all discounts work the same way, and knowing the difference can help you spot which deals are actually worth your time.

• Percentage off: The most common type. A flat percentage reduction from the listed price. Scales with the price, so it's better on expensive items.
• Dollar amount off: A fixed dollar reduction ("$10 off your purchase"). Better value on cheaper items where the dollar amount represents a higher percentage.
• Buy one, get one (BOGO): Effectively 50% off per unit when you buy two. Only a good deal if you actually need both items.
• Tiered discounts: Spend $50 get 10% off, spend $100 get 20% off, and so on. Watch out for buying more than you need just to hit the next tier.
• Clearance pricing: Usually the deepest discounts, but selection is limited and return policies may be stricter.
• Rebates: The discount comes after purchase. Factor in the hassle and the realistic chance you'll follow through before counting it as savings.

A few practical tips worth keeping in mind:

• Price-track items you want using tools like CamelCamelCamel (for Amazon) before assuming a sale price is genuinely low.
• Stack discounts strategically: apply the larger percentage first if a store lets you choose the order, since the math works out the same but it can sometimes affect which items qualify.
• Don't let a discount push you into buying something you didn't need. A 70% off deal on something you wouldn't have bought otherwise isn't savings, it's spending.
• Check whether a coupon applies before or after tax. Pre-tax discounts save you slightly more because the tax base is lower.

The best discount is the one that reduces the price of something you were already going to buy. Everything else is just math dressed up as a deal.