DigitHelm

Percentage Discount Calculator

Calculate sale price, discount amount, and savings percentage for any original price.

QUICK DISCOUNT

What Is the Percentage Discount Calculator?

This discount calculator handles three modes: find the sale price from original price and discount %, find the discount percentage from original and sale prices, and find the original price from sale price and discount %. An optional tax field shows the final total including sales tax.

  • Find Sale Price: Original price + discount % → savings and final price.
  • Find Discount %: Original and sale price → how much percent was saved.
  • Find Original Price: Sale price + discount % → what the item originally cost.
  • Tax support: Add optional sales tax to any calculation for a complete checkout total.
  • Quick discount buttons: 5%, 10%, 15%, 20%, 25%, 30%, 40%, 50%, 70%, 75% off.

Formula

Sale = Original × (1 − Discount/100)  ·  Savings = Original × Discount/100
Original = Sale ÷ (1 − Discount/100)  ·  Discount% = (Savings ÷ Original) × 100
ModeFormulaExample
Find Sale PriceOriginal × (1 − D%/100)$100 at 20% off → $80
Find Discount %(Savings / Original) × 100$100 → $75: (25/100)×100 = 25%
Find Original PriceSale ÷ (1 − D%/100)$80 after 20% off → $100
With taxSale × (1 + Tax%/100)$80 + 8.5% tax → $86.80

How to Use

  1. 1Select a mode: Find Sale Price, Find Discount %, or Find Original Price.
  2. 2Click a quick discount button or type a custom discount percentage.
  3. 3Enter the required price(s) in the input fields.
  4. 4Optionally enter a tax rate to see the total including tax.
  5. 5Press Enter or click Calculate.
  6. 6Click Clear to reset.

Example Calculation

Finding the original price from a sale

Mode: Find Original Price Sale price: $67.50 Discount: 25% Formula: Original = 67.50 / (1 − 0.25) = 67.50 / 0.75 = $90.00 Savings: $22.50 With 8% sales tax: Tax on sale price: 67.50 × 0.08 = $5.40 Total: $67.50 + $5.40 = $72.90

Common mistake: calculating discount on sale price

To find the original price, divide the sale price by (1 − discount/100). A common error is subtracting the percentage from the sale price: 67.50 − 25% of 67.50 = 50.63, that gives a different (wrong) answer because it applies the discount to the already-reduced price.

Understanding Percentage Discount

How Discounts Are Calculated

A discount reduces the price by a percentage of the original price. The key formulas are: Sale = Original × (1 − d/100) and Savings = Original × d/100. Notice that both formulas use the original price as the base, not the sale price. This distinction matters when working backwards from a discounted price.

Stacked Discounts

Two discounts applied sequentially are not additive. A 20% discount followed by a 10% further discount is not 30% off:

Original: $100 After 20% off: $80 After additional 10% off: $80 × 0.90 = $72 Total discount: (100 − 72) / 100 = 28%, not 30%

For stacked discounts, multiply the remaining fractions: (1−0.20) × (1−0.10) = 0.72 → 28% total discount. Use this calculator sequentially by entering the intermediate result into a new calculation.

Discount vs Markup

Discount and markup use different bases. A 25% discount reduces from the original price. A 25% markup increases from the cost price. They are not inverses:

  • Cost $80 with 25% markup: $80 × 1.25 = $100 retail
  • $100 retail with 25% discount: $100 × 0.75 = $75 sale (not $80)
  • To undo a 25% markup: divide by 1.25 (= 20% reduction of the retail price)
  • Gross margin = (Sale − Cost) / Sale; markup = (Sale − Cost) / Cost

Frequently Asked Questions

How do I calculate the sale price after a discount?

Use Find Sale Price mode. Formula: Sale = Original × (1 − Discount%/100).

$250 at 30% off: Sale = 250 × (1 − 0.30) = 250 × 0.70 = $175 Savings = 250 × 0.30 = $75

How do I find the original price from the sale price?

Use Find Original Price mode. Formula: Original = Sale ÷ (1 − Discount%/100).

Item on sale for $45 after 40% off: Original = 45 / (1 − 0.40) = 45 / 0.60 = $75

Never subtract the discount percentage from the sale price, that applies the discount twice. Always divide by the complement factor.

How do I calculate the discount percentage?

Use Find Discount % mode. Formula: Discount% = ((Original − Sale) / Original) × 100.

Original $120, sale $90: Discount = ((120 − 90) / 120) × 100 = (30/120) × 100 = 25%

How do I add tax to a discounted price?

Enter the tax rate in the optional Tax Rate field. Tax is applied to the sale price (after discount), then added:

$100 at 20% off → $80 sale price 8.5% sales tax: $80 × 0.085 = $6.80 Total: $80 + $6.80 = $86.80

Tax is applied after the discount, not to the original price. This is how retail checkout works in most jurisdictions.

What is the difference between a discount and a markup?

Discount reduces from retail/original price; markup increases from cost price. They use different bases:

Cost $60, 50% markup → Retail = 60 × 1.50 = $90 Retail $90, 50% discount → Sale = 90 × 0.50 = $45 (not $60!) To reverse a 50% markup: Sale = Retail / 1.50 = 90/1.50 = $60 (33.3% off retail)

How do stacked discounts work?

Sequential discounts multiply, they are not added. A 20% discount then 10% further discount is (0.80 × 0.90 = 0.72), a 28% total discount, not 30%:

$100 → 20% off → $80 → 10% off → $72 Total saved: $28 (28%, not 30%)

To combine two discounts d₁ and d₂: combined% = 100 − (1−d₁/100)×(1−d₂/100)×100

Is 50% off the same as buy-one-get-one-free?

Yes, mathematically, if you buy two items and get one free, you pay for one and get two, which is equivalent to paying 50% of the total. However, BOGO requires buying two units while "50% off" applies to one unit. The per-unit cost is the same; the total cash outlay differs.

BOGO on $20 item: Buy 2, pay $20 = $10/unit (50% off each) 50% off on $20 item: Pay $10 for one unit

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