Percentage Off Calculator: How to Calculate Discounts

The Percentage Off Formula

The math behind any discount has two parts: the savings and the sale price.

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

Or equivalently: Sale Price = Original Price − Savings.

Both formulas are identical in result. The second form is often faster because you can multiply by a single decimal instead of subtracting. Think of a 30% discount as paying 70 cents on the dollar.

Worked Examples

Example 1: 30% Off $85

Savings = $85 × 0.30 = $25.50
Sale Price = $85 − $25.50 = $59.50

Alternatively: Sale Price = $85 × 0.70 = $59.50. Same answer, one fewer step.

Example 2: 40% Off $120

Sale Price = $120 × (1 − 0.40) = $120 × 0.60 = $72.00
Savings = $120 − $72 = $48.00

How to Find the Percentage Off Given Original and Sale Price

Sometimes you want to verify whether a retailer's claimed discount is accurate. If you know both the original and sale prices:

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

Example: A jacket was $180, now $126. Discount% = ($180 − $126) ÷ $180 × 100 = $54 ÷ $180 × 100 = 30%.

You can also work backwards from a sale price to recover the original. If an item is $60 after a 25% discount:

Original Price = Sale Price ÷ (1 − Discount% / 100) = $60 ÷ 0.75 = $80.00

Stacked Discounts: Why 20% + 10% ≠ 30%

Retailers sometimes advertise a “20% off sale plus an additional 10% off with your loyalty card.” Most shoppers assume this equals 30% total. It doesn't.

Here's why. Stacked discounts apply sequentially, each to the already-reduced price:

1. Start: $100.00
2. After 20% off: $100.00 × 0.80 = $80.00
3. After additional 10% off: $80.00 × 0.90 = $72.00

Total savings: $28.00. That's a 28% effective discount, not 30%.

The formula for combined stacked discounts is:

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

For 20% + 10%: 1 − (0.80 × 0.90) = 1 − 0.72 = 0.28 = 28%.

Percentage Change: Increase vs. Decrease

Percentage off is a special case of percentage change. The general formula applies whether a price rises or falls:

% Change = (New Value − Old Value) ÷ Old Value × 100

A positive result means an increase. A negative result means a decrease (i.e., a discount).

Examples:

• Price drops from $80 to $60: ($60 − $80) ÷ $80 × 100 = −25% (a 25% discount)
• Price rises from $50 to $65: ($65 − $50) ÷ $50 × 100 = +30% (a 30% increase)

Note: a price going up 50% and then down 50% does notreturn to the original. $100 → $150 (+50%) → $75 (−50%). You end up 25% below where you started. Percentages don't cancel symmetrically.

Markup vs. Markdown: Two Very Different Calculations

These terms are often confused. The difference is what the percentage is based on.

Markup is expressed as a percentage of cost. It's used when setting a selling price:

Selling Price = Cost × (1 + Markup% / 100)

A 50% markup on a $100 cost: $100 × 1.50 = $150 selling price.

Markdown (discount) is expressed as a percentage of selling price. It's used when reducing a price:

Sale Price = Selling Price × (1 − Markdown% / 100)

A 50% markdown on that $150 selling price: $150 × 0.50 = $75— not the original $100 cost.

For a retailer to break even after a markdown, the markdown percentage must be less than the markup percentage. A 50% markup and a 50% markdown results in a $25 loss on a $100-cost item.

Retailer Pricing Psychology: The Anchoring Effect

“Was $100, now $79.99.” You've seen this thousands of times. The crossed-out original price is not just informational — it's a cognitive lever.

Behavioral economist Dan Ariely demonstrated in his research on anchoring that the first number a buyer sees acts as an anchor, biasing every subsequent judgment of value. The “was” price doesn't need to be real to be effective. It just needs to be present.

This is why retailers set inflated “original” prices before a sale. The actual discount might be 10% on a price that was already inflated by 30% over the market rate. Your $20 savings could be illusory.

The FTC has guidelines requiring that “was” prices represent a genuine prior selling price — but enforcement is uneven, and the practice remains common.

Black Friday Math: What You're Actually Saving

Black Friday advertising is saturated with “50% off,” “70% off,” and “biggest sale of the year” claims. The reality is more modest.

According to the National Retail Federation (NRF), the average Black Friday discount on electronics and major categories typically falls between 15% and 25%— not the 50–70% figures that dominate advertising. Many “deals” are available at the same price year-round or represent temporary price inflation followed by a cut.

Genuine deep discounts (40%+) do exist, but they're concentrated in specific categories: leftover seasonal items, last year's electronics models, and overstock clearance. Knowing the formula for real discount percentage lets you cut through the noise and verify what you're actually saving.

BOGO: The 50% Discount That Sounds Like 100%

“Buy One Get One Free” feels like getting something for nothing. But when you're buying two items, the true discount is straightforward:

You pay for 1 item, you receive 2. Cost per item = Original Price ÷ 2. Savings per item = 50%.

The effective discount is 50% when purchasing two units, not 100% off any single item in isolation. It's only a good deal if you were going to buy two anyway.

BOGO 50% off (buy one, get the second at half price) works out to just 25% total savings on two items:

• Item 1: full price $50
• Item 2: 50% off = $25
• Total paid: $75 vs. $100 full price → 25% savings

How to Verify a Real Discount

Before buying something “on sale,” spend 90 seconds checking whether the discount is genuine:

1. Check price history. For Amazon products, CamelCamelCamel shows the full price history graph. Many Amazon “Lightning Deals” are at prices identical to last month.
2. Google the product + “price.” Comparison shopping engines like Google Shopping, PriceGrabber, and Shopzilla show current prices across retailers instantly.
3. Check the original price date. A “was $200” price that was only active for one day two months ago is not a genuine reference price.
4. Calculate it yourself. Use the formula: Discount% = (Original − Sale) ÷ Original × 100. If the math doesn't match the advertised percentage, that's a red flag.
5. Consider the base rate. A 10% discount on an already-overpriced item isn't a deal. Compare the sale price to the market rate, not just the store's “original” price.

Frequently Asked Questions

How do you calculate percentage off?

Multiply the original price by the discount as a decimal, then subtract from the original. For 30% off $85: Savings = $85 × 0.30 = $25.50; Sale Price = $85 − $25.50 = $59.50. Faster shortcut: Sale Price = $85 × 0.70 = $59.50.

How do I find the original price after a percentage off?

Divide the sale price by (1 minus the discount as a decimal). If an item is $60 after 25% off: Original Price = $60 ÷ (1 − 0.25) = $60 ÷ 0.75 = $80.00. This works for any discount percentage.

What is a stacked discount?

A stacked discount applies two or more discounts sequentially, each calculated on the price after the previous discount. A 20% off coupon plus an additional 10% off on a $100 item: $100 × 0.80 = $80, then $80 × 0.90 = $72. The effective discount is 28%, not 30%. The formula: Effective Discount% = 1 − (1 − D1/100) × (1 − D2/100).

What is the difference between markup and markdown?

Markup is the percentage of cost added to set a selling price. Markdown is the percentage of selling priceremoved for a discount. A 50% markup on $100 cost = $150 price. A 50% markdown on $150 = $75 — well below the original cost. They're calculated on different bases, so the same percentage produces very different numbers.

How do I calculate percentage change (increase or decrease)?

% Change = (New Value − Old Value) ÷ Old Value × 100. A positive result is an increase; negative is a decrease. If a price rises from $50 to $65: % Change = ($65 − $50) ÷ $50 × 100 = +30%. If it falls from $80 to $60: % Change = ($60 − $80) ÷ $80 × 100 = −25%.