How to Calculate a Discount — Shopping Maths Made Simple

TL;DR

Discounted price = Original Price × (1 − Discount %). A $200 item at 30% off costs $140.
Stacked discounts do not add up. 20% off then 10% off equals 28% off total, not 30%.
Reverse calculation: if you know the sale price, divide by (1 − discount %) to find the original.
Use allcalculator.biz for instant results. No login, no app, works from any phone at the checkout.
41%
actual saving when a '50% off
then 20% off' deal is stacked
0 sec
time to verify a price with
a free online calculator
$1,040
avg annual saving for shoppers who
check unit prices every week

Why Most People Get Discount Maths Wrong

You see a sign that says 50% off. Then at the checkout there is another 20% off with a code. You assume you are paying 30% of the original price.

You are not. You are paying 40%.

Those two discounts do not add up. Each one applies to the already reduced price. That difference 10 percentage points on a big purchase is real money.

This guide covers every discount calculation you will actually encounter. The formulas are simple. The examples use real numbers.

The BASIC DISCOUNT FORMULA

Start here. This handles most real-world situations.

Discounted Price = Original Price × (1 − Discount %).

Convert the percentage to a decimal first. 25% becomes 0.25. Subtract it from 1 and you get the fraction you actually pay.

Example: A $180 jacket at 25% off.

  1. 25% as a decimal = 0.25
  2. 1 − 0.25 = 0.75
  3. $180 × 0.75 = $135
  4. You pay $135. You save $45.

If you want to calculate the saving separately:

Saving = Original Price × Discount %

$180 × 0.25 = $45 saved.

How Stacked Discounts Actually Work

This is the one most people get wrong.

A shoe store has 30% off everything. You also have a member code for 15% off. You might think that is 45% off total.

It is not.

Each discount applies to the running price at that point, not the original.

  1. Start: $220
  2. 30% off: $220 × 0.70 = $154
  3. 15% off the new price: $154 × 0.85 = $130.90
  4. Total saving: $220 − $130.90 = $89.10
  5. Actual discount: $89.10 ÷ $220 × 100 = 40.5%, not 45%

The formula for combined discount percentage:

Combined % = 1 − ((1 − D1) × (1 − D2))

Example: 0.30 and 0.15 stacked → 1 − (0.70 × 0.85) = 1 − 0.595 = 40.5% total discount.

The order of stacked discounts does not matter. 30% then 15% gives the same final price as 15% then 30%. What changes is the intermediate price, not the end result.

How To Reverse Calculate The Original Price

You are at a sale. The price tag shows $85. The sign says 40% off. What was the original price?

Most people try to add 40% back on. That gives the wrong answer.

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

$85 ÷ (1 − 0.40) = $85 ÷ 0.60 = $141.67

Adding 40% to $85 would give you $119. That is wrong. The correct original is $141.67.

This matters when you want to verify whether a stated 'original price' is accurate.

Was The 'Original Price' Real?

Retailers sometimes inflate the 'was' price to make the discount look bigger. The rule in Australia requires that the 'was' price must have been the genuine selling price for a reasonable period before the sale.

The best way to check is to compare against a competitor who is not running a sale.

True Saving % = ((Competitor Price − Sale Price) ÷ Competitor Price) × 100

Example: A store advertises a laptop at $999, down from $1,499. The same laptop is $1,150 at another retailer.

  1. True saving: $1,150 − $999 = $151
  2. True saving %: $151 ÷ $1,150 × 100 = 13.1%
  3. Claimed saving: 33%
  4. Reality: you are saving about 13 cents in the dollar, not 33

For a refresher on the percentage formula behind these calculations, see: how to calculate percentage — a simple guide.

Discount Type What It Means How to Calculate
Percentage off A flat % reduction on the price Price × (1 – %)
Fixed amount off $X removed from the price Original − Amount
Buy one get one free Second item is free Pay for 1, effective 50% per item
Buy 2 get 1 free Third item is free across 3 Pay for 2 of 3, effective 33.3% per item
Cashback Refund after purchase Same end cost if cashback is guaranteed
Loyalty points Points redeemable as cash later Convert points to dollar value first, then compare

Unit Price: The Discount Check Most People Skip

Supermarkets and online stores use different pack sizes to make comparisons hard. A bigger pack is not always better value.

Unit Price = Total Price ÷ Quantity

Discount Types Explained, And How To Calculate Each One

Discount Type What It Means How to Calculate
Percentage off A flat % reduction on the price Price × (1 – %)
Fixed amount off $X removed from the price Original − Amount
Buy one get one free Second item is free Pay for 1, effective 50% per item
Buy 2 get 1 free Third item is free across 3 Pay for 2 of 3, effective 33.3% per item
Cashback Refund after purchase Same end cost if cashback is guaranteed
Loyalty points Points redeemable as cash later Convert points to dollar value first, then compare

Unit Price: The Discount Check Most People Skip

Supermarkets and online stores use different pack sizes to make comparisons hard. A bigger pack is not always better value.

Unit Price = Total Price ÷ Quantity

Example: Two packs of washing powder.

This calculation is simple. Most people skip it because it requires division. A calculator removes that friction in seconds.

Quick Mental Shortcuts For Common Discounts

For rough estimates at the shelf, these shortcuts are fast enough without a calculator.

More of these in our post on maths tricks to do quick calculations in your head.

GST And Discounts In Australia

Discounts in Australia apply to the GST inclusive price. So, the saving is calculated on the total price you see on the shelf, GST included.

Example: A $110 item (which includes 10% GST) at 20% off.

  1. $110 × 0.80 = $88 final price
  2. The $88 still includes GST
  3. GST portion of $88 = $88 ÷ 11 = $8

For business buyers: you claim GST credits on the price you actually paid, not the pre discount price. If you paid $88, you claim back $8 in GST, not the $10 that would have applied to the full $110.

How To Use A Calculator To Check Discounts In Store

You do not need a fancy app. A basic calculator on your phone is enough.

  1. Type the original price
  2. Multiply by (1 minus the discount as a decimal).For 30% off: multiply by 0.70
  3. The result is what you pay.

For stacked discounts, do it twice. First discount, note the result, then apply the second discount to that result.

Our free calculator at allcalculator.biz handles this directly. Type in the numbers, get the answer. No login, no app download, works from any phone at the checkout.

A 5 second check at the shelf can tell you whether a 'sale' price is actually competitive. Most people skip it because they assume the maths is complicated. It is not.

Common Discount Mistakes

✕ Assuming stacked discounts add up. They do not. 20% + 10% = 28% off, not 30%.

✕ Adding the discount % back on to find the original price. That gives the wrong number. Divide by (1 − %) instead.

✕ Comparing prices from different base quantities without calculating unit price first.

✕ Taking 'was/now' prices at face value without comparing to a competitor.

✓ Calculating the unit price before deciding between pack sizes.

✓ Using a calculator in store before committing to a purchase above $50.

✓ Checking whether a 'sale' price is actually cheaper than a competitor's regular price.

Frequently Asked Questions

Does 20% off then 10% off equal 30% off?

No. Stacked discounts do not add up. 20% off reduces the price to 80% of the original. The subsequent 10% off applies to that reduced price, not the original. The combined discount is 28%, not 30%. The formula is: 1 − (0.80 × 0.90) = 0.28 or 28%.

How do I find the original price if I only know the sale price and the discount?

Divide the sale price by (1 − the discount as a decimal). If an item is $68 after a 15% discount: $68 ÷ 0.85 = $80. Many people incorrectly add 15% back on, which gives $78.20, that is the wrong answer.

Is a higher discount always a better deal?

Not necessarily. The discount is only as meaningful as the starting price. A 60% discount on an inflated original price may cost more than a 10% discount on a competitively priced item. Always compare the final price against what the same product costs elsewhere.

How do cashback offers compare to direct discounts?

A cashback offers returns money after the purchase. A direct discount reduces the price at the point of sale. If the cashback is guaranteed and arrives quickly, the financial outcome is equivalent. The practical difference is that a discount is certain and immediate. Cashback has conditions, processing delays, and sometimes minimum thresholds before it pays out.

Related Reading

These posts go well with what you have just read:

The next time you see a sale sign, you will know what it actually means not just what it is trying to make you feel.