How to Find the Original Price Before a Percentage Discount

One of the most misunderstood percentage calculations is working backwards from a discounted price to find the original. Most people instinctively add the discount percentage back, which gives the wrong answer every time.
Here is the correct formula, four worked examples, and a JavaScript function you can use directly in your projects.

Why Adding the Percentage Back Is Wrong

A product is $85 after a 15% discount. Most people try:
$85 + 15% of $85 = $85 + $12.75 = $97.75 ❌
Wrong. The original price was $100, not $97.75.
The reason: the 15% discount was calculated on the original price, not the sale price. So you cannot simply reverse it by adding 15% to the sale price.

The Correct Formula

Original price = Sale price ÷ (1 − discount as decimal)
For a price increase (finding original before a markup):
Original price = Final price ÷ (1 + increase as decimal)

Example 1 - Retail Discount

Sale price: $85
Discount: 15%

Original = $85 ÷ (1 − 0.15)
Original = $85 ÷ 0.85
Original = $100 ✅

Example 2 - Higher Discount

Sale price: $60
Discount: 40%

Original = $60 ÷ (1 − 0.40)
Original = $60 ÷ 0.60
Original = $100 ✅

Example 3 - Finding Original Before a Tax Was Added

Price including 20% VAT: $120

Original (ex-VAT) = $120 ÷ (1 + 0.20)
Original = $120 ÷ 1.20
Original = $100 ✅

Example 4 - Salary Before a Raise

Current salary: $52,500 (after a 5% raise)

Original = $52,500 ÷ (1 + 0.05)
Original = $52,500 ÷ 1.05
Original = $50,000 ✅

JavaScript Implementation

Here is a clean utility function you can use in any project:


/**
 * Find original value before a percentage change was applied
 * @param {number} finalValue - The value after the change
 * @param {number} percentage - The percentage that was applied (positive for increase, negative for decrease)
 * @returns {number} The original value before the change
 */
function findOriginalValue(finalValue, percentage) {
  if (percentage === -100) {
    throw new Error('Cannot reverse a 100% decrease');
  }
  return finalValue / (1 + percentage / 100);
}

// Examples
findOriginalValue(85, -15);   // 100 (original before 15% discount)
findOriginalValue(120, 20);   // 100 (original before 20% VAT)
findOriginalValue(52500, 5);  // 50000 (salary before 5% raise)

Handling Edge Cases

function findOriginalValue(finalValue, percentage) {
  // Guard against division by zero
  if (percentage === -100) {
    throw new Error('Cannot reverse a 100% decrease - original was zero');
  }

  // Guard against invalid inputs
  if (typeof finalValue !== 'number' || typeof percentage !== 'number') {
    throw new TypeError('Both arguments must be numbers');
  }

  const multiplier = 1 + percentage / 100;
  return Math.round((finalValue / multiplier) * 100) / 100; // Round to 2 decimal places
}

Where This Comes Up in Real Projects

E-commerce: Displaying original prices alongside sale prices
Tax calculators: Stripping VAT/GST from inclusive prices
Payroll systems: Calculating pre-raise salary from current salary
Pricing engines: Reversing markup to find wholesale cost
Financial apps: Finding pre-interest principal amounts

Skip the Manual Calculation

For quick reverse percentage calculations without writing code, https://onlinepercentage.net has a dedicated reverse percentage mode. Enter the final value and the percentage, the original value appears instantly. Free, no sign-up needed.

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