# Discount Calculator Use our free discount calculator to find the sale price, savings, and discount percentage. Shows step-by-step work for any type of discount. --- - **Canonical URL:** https://dothecalculation.com/calculators/discount-calculator - **Category:** Business tools - **Publisher:** Do The Calculation (https://dothecalculation.com) - **Cost:** Free, no account or sign-up required - **Privacy:** Runs entirely in the browser; inputs are never sent to a server - **Methodology:** https://dothecalculation.com/methodology --- ## Calculate discount savings and sale price Estimate amount saved, final sale price, and effective percentage reductions from promotions or markdowns. - Original vs discounted price - Savings amount calculation - Promotion comparison view ## Discounts as price reductions A discount is a reduction from the original listed price. In consumer retail, discounts are typically expressed as a percentage off the original amount. In business invoicing, discounts may represent promotional markdowns, early-payment incentives, or negotiated trade reductions. The key conceptual point is that the discount percentage is applied to the original base price, not the final price. This means the amount saved depends directly on the starting value. ## The discount formulas The amount saved is: $$\text{Savings} = \text{Original Price} \times \frac{\text{Discount Rate}}{100}$$ The final sale price is: $$\text{Final Price} = \text{Original Price} - \text{Savings}$$ Equivalently: $$\text{Final Price} = \text{Original Price} \times \left(1 - \frac{\text{Discount Rate}}{100}\right)$$ If a $250 item is discounted by 20%, the savings are $50 and the final sale price is $200. ## Stacked discounts and effective rates Multiple discounts are not added directly unless they are applied simultaneously to the original base. If an item receives 20% off and then another 10% off, the second discount applies to the already reduced price. This makes the effective overall discount less than 30%. Sequential discounting is multiplicative, not additive. ## Discounts, taxes, and invoice sequencing In many systems, discounts are applied before tax. This means the tax is calculated on the reduced taxable amount, not the original gross figure. Businesses should define discount sequencing clearly to avoid accidental overcharging or understating revenue. ## Worked example: 30% off, plus a code, plus tax A jacket lists at £180. The sale is 30% off, a newsletter code takes a further 15%, and VAT at 20% is already included in the shelf price. **Step 1 — first discount.** 180 × 0.30 = £54 off, leaving 180 − 54 = **£126**. **Step 2 — second discount, applied to the new price.** 126 × 0.15 = £18.90 off, leaving **£107.10**. **Step 3 — the effective rate.** Total saved is 180 − 107.10 = £72.90, so the effective discount is 72.90 ÷ 180 = **40.5%**, not the 45% you get by adding 30 and 15. The shortcut is 1 − (0.70 × 0.85) = 1 − 0.595 = 40.5%; stacked discounts always multiply, and always come out below the sum. **Step 4 — separating the tax.** Because VAT is included, the net price is 107.10 ÷ 1.20 = **£89.25**, and the VAT element is £17.85. Dividing by 1.20 is correct here; subtracting 20% is not, and would understate the net figure by £3.57. ## Reverse calculations: original price and discount rate Two questions come up as often as the forward calculation, and both are one rearrangement away. **Finding the original price from a sale price.** If an item is £68 after 20% off, divide rather than add back: 68 ÷ (1 − 0.20) = 68 ÷ 0.80 = **£85**. Adding 20% to £68 gives £81.60, which is wrong, because the 20% was a percentage of the larger original figure, not of the sale price. **Finding the discount rate from two prices.** With an original of £250 and a sale price of £185, the rate is (250 − 185) ÷ 250 = 65 ÷ 250 = **26%**. Always divide the saving by the original, never by the sale price — dividing by 185 would report 35.1% and overstate the deal. This asymmetry is why a 50% rise followed by a 50% fall does not return you to where you started, and why "was £200, now £100, that's 100% off" is a mis-statement: the discount is 50%, while the markup needed to go back the other way is 100%. ## What a discount does to your margin From the seller's side, the important number is not the discount percentage but the volume needed to stand still. If an item costs £60 and sells at £100, the margin is 40% and the gross profit is £40. Discount by 20% and the price becomes £80, so the profit is £20 — half of what it was. To hold total gross profit flat, unit sales must **double**. The general relationship is: required volume increase = discount ÷ (margin − discount), with both as decimals. At a 40% margin, a 10% discount needs 33% more volume; a 20% discount needs 100% more. At a 25% margin, a 10% discount already needs 67% more volume, and a discount of 25% or more makes the arithmetic impossible because there is no margin left to sell into. This is why deep discounting works for clearing stock, whose alternative is a write-off, and rarely works as a growth strategy. Before setting a promotional rate, run it against your actual gross margin after cost of goods, shipping, payment fees and expected returns — a 20% promotion on a 25% margin is close to selling at cost once fees are counted. ## Frequently asked questions ### How do I calculate a discount? Multiply the original price by the discount rate to get savings, then subtract the savings from the original price. ### What is the formula for sale price? Final Price = Original Price × (1 - Discount Rate / 100). ### What is the amount saved? It is the difference between the original price and the discounted final price. ### Are two 10% discounts the same as one 20% discount? No. Sequential discounts compound on the reduced price, so the effective total reduction is smaller than a simple sum. ### Should sales tax be applied before or after discount? In many cases tax is applied after the discount, but local rules vary and should be verified. ### What is an effective discount rate? It is the overall percentage reduction achieved after one or multiple markdowns are applied. ### Can the discount amount be larger than the original price? Not in a standard pricing model. A discount above 100% would imply a negative price and is not a normal sale calculation. ### What if the discount is zero? Then the final price equals the original price and the amount saved is zero. ### How do markdowns affect margin? Discounts reduce revenue while cost usually stays fixed, so margin percentages fall quickly when markdowns increase. ### Why are discounts expressed as percentages? Percentages scale across prices, allowing shoppers and businesses to compare reductions across items of different values. ## Related concepts - **Markdown** — A deliberate reduction in listed price to stimulate sales or clear inventory. - **Effective discount** — The true overall reduction after applying one or more discount stages. - **Taxable amount** — The base price remaining after any discount adjustments, before tax is applied. ## Related guides - [Discount Calculator: A Complete Guide to Calculating Discount Percentage](https://dothecalculation.com/blog/business/discount-percentage-complete-guide) — Master discount math with step-by-step formulas for sale price, discount percentage, and original price, plus stacked discounts, fake discount red flags, and practice problems. - [Discount, Markup, and Margin: A Practical Pricing Guide](https://dothecalculation.com/blog/business/discount-markup-strategy) — Calculate sale price, markup, and margin, then test how a discount changes unit profit, required sales volume, and the economics of a promotion. - [Stacked Discounts & BOGO Deals: How to Tell If a Combo Deal Really Saves You Money](https://dothecalculation.com/blog/business/stacked-discounts-bogo-deals-guide) — A "40% off, plus an extra 15% at checkout" sign is not 55% off. Learn the real math behind stacked discounts and BOGO deals, with worked examples, charts, and a quick framework for spotting a deal that only looks good. - [How to Build a Discount Calculator in Excel and Google Sheets (Formulas Explained)](https://dothecalculation.com/blog/templates/discount-calculator-excel-google-sheets-guide) — Every discount calculation — percentage off, stacked discounts, reverse original-price lookups, and tiered bulk pricing — comes down to a handful of one-line formulas. Here is exactly how to set them up. - [Discount Then Tax: How to Calculate Your Real Final Price (and When Order Actually Matters)](https://dothecalculation.com/blog/business/discount-then-tax-final-price-guide) — Most guides say "always apply the discount before tax," as if the order changes the total. For a percentage discount it never does — multiplication does not care what order it happens in. Here is the real rule, the one case where order genuinely changes your total, and the formulas for both. - [Percentage Change Guide: Increase, Decrease, Difference](https://dothecalculation.com/blog/math/percentage-change-calculation) — Learn when to use percent of, percent change, and percent difference with worked examples tied to the live DTC percentage calculator. ## Related calculators - [Markup Calculator](https://dothecalculation.com/calculators/markup-calculator) — Calculate markup percentage and profit margin from cost and selling price to set prices that guarantee your target profit on every sale. - [Overhead Rate Calculator](https://dothecalculation.com/calculators/overhead-rate-calculator) — Calculate your business overhead rate as a percentage of sales or labor cost to price products and services effectively and profitably. - [Cohort SaaS LTV Calculator](https://dothecalculation.com/calculators/saas-ltv-cohort-calculator) — Calculate customer lifetime value using cohort-specific retention curves, discount rates, and average monthly subscription price. - [Cohort Customer Lifetime Value (LTV) Calculator](https://dothecalculation.com/calculators/customer-lifetime-value-detailed-calculator) — Model customer lifetime value using discount rate, average order value, purchase frequency, and retention rate for cohort-based forecasting. - [Freelance Rate Calculator](https://dothecalculation.com/calculators/freelance-rate-calculator) — Calculate your ideal freelance hourly and project rates from income goals, expenses, and billable hours to price your work with confidence. - [Freelance Tax Deduction Calculator](https://dothecalculation.com/calculators/freelance-tax-deductions-calculator) — Estimate tax savings from eligible business expense write-offs to help freelancers and self-employed workers lower their taxable income. --- _This calculator is for educational and business planning purposes only. Discount, GST, VAT, invoicing, and pricing decisions may require accounting, legal, or tax review depending on your jurisdiction and industry._ --- _Source: [Do The Calculation](https://dothecalculation.com/calculators/discount-calculator). Quote freely with attribution and a link to this page._