Discount Guide: Formulas, Deal Comparisons + Mini Calculators

Learn how discounts really work (percent off, fixed amount off, Buy X Get Y, stacked discounts) — with interactive mini calculators in each section.

Examples-firstDeal mathInteractive mini-calcs
10 min read•Last updated Jan 13, 2026

What is a Discount?

A discount is the difference between the original price and what you actually pay.

In deal math, you almost always care about two values: the original (list) price and the final (paid) price. Everything else is derived from those.

The simplest definitions are: savings = original − final and discount% = (savings ÷ original) × 100. Once you keep those straight, you can compare almost any promotion.

Everyday example
  • Original: 1,999
  • Final: 1,499
  • Savings: 500
  • Discount%: (500 ÷ 1,999) × 100 ≈ 25.01%

Summary

Original
$1,999.00
Final
$1,499.00
You save
$500.00
Effective discount
25.01%
Open full Discount Calculator →
Your mental model: price → pay → savings
When comparing deals, compute the final price first. A “bigger percent” is not always better if the base price differs or if restrictions apply.
Key takeaway
Discount is best understood via final price and savings.

Percent Off (% off)

A percent-off discount reduces the price by a fraction of the original: final = original × (1 − p/100).

A “p% off” deal means you pay the remaining (100 − p)%. So 15% off means you pay 85% of the original price.

If multiple items are involved, compute per-item and total carefully. Some stores apply “X% off” only to certain items (like every 2nd item, or the cheapest item).

Percent-off example
  • Original: 1,449
  • Discount: 15%
  • Final: 1,449 × 0.85 = 1,231.65
  • Savings: 217.35
Open full Discount Calculator →
Percent-off is multiplicative, not subtractive
A 20% off deal is not the same as subtracting 20 currency units. Percent is always relative to the original price.
Key takeaway
Percent off: final = original × (1 − p/100).

Fixed Amount Off

Fixed-off deals subtract a constant amount: final = max(0, original − amountOff).

A fixed discount reduces the price by the same amount regardless of the original price. This makes it easy to compare against percent-off by converting to an effective discount%.

Be careful with edge cases: the final price can’t go below 0, and some promotions have minimum spend requirements (not modeled here).

Fixed-off example
  • Original: 999
  • Amount off: 200
  • Final: 999 − 200 = 799
  • Effective discount%: (200 ÷ 999) × 100 ≈ 20.02%
Open full Discount Calculator →
Key takeaway
Fixed-off: final = max(0, original − off).

Buy X Get Y Free

BxGy discounts change the effective unit price: you pay for X items and receive X+Y items.

For a Buy X Get Y deal at a consistent unit price, the effective discount is based on the fraction of items you pay for.

Example: Buy 2 get 1 free → you pay for 2 out of 3 items, so the effective discount is 1/3 ≈ 33.33% (assuming equal price and all items qualify).

B2G1 example
  • Unit price: 149
  • Deal: Buy 2 get 1 free
  • Total items: 3, paid items: 2
  • Effective discount%: 1 ÷ 3 × 100 = 33.33%
Open full Discount Calculator →
Cheapest-item rules can change the math
Many stores apply “free” items as the cheapest eligible items. If prices vary, compute using the actual discount application rule.
Key takeaway
BxGy (equal-price): effective discount% ≈ Y ÷ (X+Y) × 100.

Stacked Discounts (10% + 20%)

Stacked percent discounts apply sequentially: final = original × (1 − p1) × (1 − p2) ...

A very common mistake is adding discount percentages. 10% + 20% is not 30% off when applied sequentially; it is 28% off because the second discount applies to the already-reduced price.

The safe way: multiply the remaining fractions. For 10% then 20%: pay 90% then 80% → pay 0.9 × 0.8 = 0.72 → 28% total discount.

Stacked example
  • Original: 2,000
  • Discounts: 10% then 20%
  • Final: 2,000 × 0.9 × 0.8 = 1,440
  • Effective discount%: (2,000 − 1,440) ÷ 2,000 = 28%
Open full Discount Calculator →
Shortcut for two discounts
Total discount% = 1 − (1 − p1)(1 − p2). For 10% and 20%: 1 − 0.9×0.8 = 28%.
Key takeaway
Stacked %: multiply remaining fractions; don’t add percents.

Effective Discount (when you know final price)

If you know original and final, compute the effective discount% directly.

Sometimes a promotion is complicated (coupon + shipping + bundle rules). If you can compute the final price, you can always compute the effective discount% for comparison.

This is the best way to compare two different-looking deals: reduce each to final price and savings.

Effective discount example
  • Original: 5,000
  • Final: 3,999
  • Savings: 1,001
  • Effective discount%: (1,001 ÷ 5,000) × 100 = 20.02%

Summary

Original
$1,999.00
Final
$1,499.00
You save
$500.00
Effective discount
25.01%
Open full Discount Calculator →
Key takeaway
Effective discount% = (original − final) ÷ original × 100.

Compare Deals Quickly

Convert every deal into final price and effective discount%.

A 20% off deal on an inflated list price may be worse than a smaller percent on a lower price. For bundles and BxGy, compute the per-item final price.

If deals have constraints (like “only on 2nd item”), compute totals for the quantity you actually intend to buy.

Comparison example
  • Deal A: 25% off on 1,600 → final 1,200
  • Deal B: 200 off on 1,300 → final 1,100
  • Deal B is cheaper even though its percent is smaller.
Open full Discount Calculator →
Decision rule
Pick the deal with the lower final price for your basket (unless quality/returns differ). Effective discount% is helpful, but final price is what you pay.
Key takeaway
Final price beats “headline percent” for comparisons.

Common Mistakes

Most errors come from adding percents or ignoring how promos apply to items.

Don’t add stacked discounts (10% + 20% ≠ 30%). Apply sequentially.

For BxGy deals, confirm whether items have equal prices or if the store applies the discount to the cheapest eligible item.

For “Nth item” promos, model the actual quantity you’re buying. The effective discount depends on basket size.

Mistake example
  • Wrong: 10% + 20% = 30%
  • Right: pay 0.9 then 0.8 → pay 0.72 → 28% off
Key takeaway
Model the basket; apply discounts the way the store applies them.

Quick Reference

Keep these formulas handy for most discount scenarios.

These are the formulas used by the mini calculators and the full Discount Calculator.

Reference
  • Use these to sanity-check any promo.
Discount formulas
ScenarioFinal priceSavingsEffective discount%
Percent off (p%)original × (1 − p/100)original − final(savings ÷ original) × 100
Fixed off (d)max(0, original − d)original − final(savings ÷ original) × 100
BxGy (equal price)unit × X/(X+Y) × (X+Y)unit × YY ÷ (X+Y) × 100
Stacked percentsoriginal × Π(1 − pᵢ/100)original − final(savings ÷ original) × 100
Key takeaway
Reduce every deal to final price + savings.

FAQs

Is 10% + 20% the same as 30% off?
No. If applied sequentially, 10% then 20% means you pay 0.9 × 0.8 = 0.72 of the original price, which is 28% off.
How do I compare Buy 2 Get 1 free vs 33% off?
If all items are equal price and you buy in groups of 3, Buy 2 Get 1 is exactly 33.33% off. If prices vary or the promo applies to the cheapest item, compute using the store rule.
What is “effective discount” and why does it matter?
Effective discount is the true percent you saved relative to original price: (original − final) ÷ original × 100. It lets you compare different-looking deals fairly.
Can a fixed amount off be better than a percent off?
Yes. A fixed discount is a larger percent when the original price is small. Convert the fixed amount to an effective percent to compare.
Related
Open the full Discount CalculatorPercentage GuidePercentage Calculator
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Want to compare more promo types?

Open the full Discount Calculator to model stacked discounts, Buy X Get Y, and itemized carts.

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