Most percentage questions go forward: you know the original number and the percentage, and you want the result. Reverse percentage flips that: you know the result, and you want to find the original number it came from.<\/p>\n
To find an original value before a percentage decrease (like a discount) was applied:<\/p>\n
Original = Result \u00f7 (1 \u2212 Percentage \u00f7 100)<\/strong><\/p>\n For a percentage increase (like tax added), subtract becomes add:<\/p>\n Original = Result \u00f7 (1 + Percentage \u00f7 100)<\/strong><\/p>\n You see a jacket on sale for $68, marked as “15% off.” What was it before the discount?<\/p>\n Original = $68 \u00f7 (1 \u2212 0.15) = $68 \u00f7 0.85 = $80<\/strong><\/p>\n A common mistake here is calculating 15% of $68 and adding it back ($68 + $10.20 = $78.20), which is wrong, because 15% of the *original* price was removed, not 15% of the sale price. The two numbers are different because the discount percentage applies to a different base.<\/p>\n A receipt shows a total of $53.50 including 7% sales tax. What was the price before tax?<\/p>\n Original = $53.50 \u00f7 (1 + 0.07) = $53.50 \u00f7 1.07 = $50.00<\/strong><\/p>\n Beyond shopping, this same math shows up in payroll (working out gross pay from a net figure after a known deduction rate), business pricing (reverse-engineering a cost basis from a marked-up retail price), and comparing sales across stores where only the final price is shown.<\/p>\n Our Reverse Percentage Calculator<\/a> does this calculation instantly for both the discount and tax-inclusive cases above.<\/p>\n Divide the sale price by (1 \u2212 discount rate). A $68 item marked 15% off was originally $68 \u00f7 0.85 = $80.<\/p>\n Divide the total by (1 + tax rate). A $53.50 total with 7% sales tax was $53.50 \u00f7 1.07 = $50.00 before tax.<\/p>\n Because the discount was a percentage of the original price, not the sale price. Adding 15% of $68 gives $78.20, which undershoots the true original of $80.<\/p>\n If you only know a discounted price, here’s the formula to work backward to the original price, with a worked example and the tax-inclusive version too.<\/p>\n","protected":false},"author":1,"featured_media":1024,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15],"tags":[],"class_list":["post-92","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-percentages-shopping-math"],"_links":{"self":[{"href":"https:\/\/thenesttools.com\/blog\/wp-json\/wp\/v2\/posts\/92","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/thenesttools.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/thenesttools.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/thenesttools.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/thenesttools.com\/blog\/wp-json\/wp\/v2\/comments?post=92"}],"version-history":[{"count":3,"href":"https:\/\/thenesttools.com\/blog\/wp-json\/wp\/v2\/posts\/92\/revisions"}],"predecessor-version":[{"id":203,"href":"https:\/\/thenesttools.com\/blog\/wp-json\/wp\/v2\/posts\/92\/revisions\/203"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/thenesttools.com\/blog\/wp-json\/wp\/v2\/media\/1024"}],"wp:attachment":[{"href":"https:\/\/thenesttools.com\/blog\/wp-json\/wp\/v2\/media?parent=92"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thenesttools.com\/blog\/wp-json\/wp\/v2\/categories?post=92"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thenesttools.com\/blog\/wp-json\/wp\/v2\/tags?post=92"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Worked example: finding the price before a discount<\/h2>\n
Worked example: finding the pre-tax price<\/h2>\n
Why this comes up more than you’d think<\/h2>\n
Frequently Asked Questions<\/h2>\n
How do you find the original price after a discount?<\/h3>\n
How do you remove sales tax from a total?<\/h3>\n
Why can’t I just add the discount percentage back on?<\/h3>\n
Related Reading<\/h2>\n
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