Skip to content
CalculatorGeek

Reverse Percentage Decrease: Find the Original Value

On this page

Direct answer

If a final value is p percent below the original, divide the final value by 1 − p/100. Do not simply add p percent to the reduced value.

Formula and method

Original = final ÷ (1 − percentage decrease ÷ 100)

This page must show the formula exactly as the calculator or worked method uses it. Inputs remain unrounded during the calculation; rounding applies only to the displayed answer unless a domain-specific rule requires otherwise.

Step-by-step calculation

  1. Convert the decrease rate to a decimal.
  2. Subtract it from 1 to get the remaining fraction.
  3. Divide the final value by that fraction.
  4. Check by applying the decrease to the recovered original.

Worked examples

Sale price

$72 after 20% off: 72 ÷ 0.80 = $90.

Reduced headcount

460 after an 8% decrease: 460 ÷ 0.92 = 500.

Why adding fails

$72 × 1.20 = $86.40, not $90, because the 20% increase uses $72 as its baseline.

Interpretation and edge cases

  • A 100% decrease leaves zero, so a unique original cannot be recovered from the final value alone.
  • Use the unrounded final value where possible.
  • A displayed sale price may contain currency rounding.

Frequently asked questions

How do I undo a 25% decrease?

Divide by 0.75.

Why not multiply by 1.25?

Because the decrease and recovery use different baselines.

Can the original be found after a 100% decrease?

No; every original maps to zero.

Sources and transparency

The formulas and examples were evidence-checked on 2026-09-10. This is educational mathematical content. It does not replace a field-specific standard, accounting policy, laboratory method, contractual definition or professional judgment. CalculatorGeek should display a named human reviewer only after a real reviewer has completed and documented that review.

Use this resource

1 available tool
Open the Percentage Decrease CalculatorRun the calculation with your own inputs, then return here to interpret it.

Keep exploring

4 available tools
Successive Percentage Decreases and Stacked DiscountsCombine two or more percentage decreases correctly with multipliers. See stacked-discount examples and the equivalent total decrease.Percentage Decrease vs Percent ChangeLearn when to use percentage decrease and when to use signed percent change, including baselines, formulas and zero-value limits.Percentage Decrease in Excel and Google SheetsUse percentage decrease formulas in Excel or Google Sheets. Includes zero-safe formulas, formatting, reverse calculations and stacked decreases.Percentage Decrease ExamplesWork through percentage decrease examples for prices, budgets, inventory, traffic and measurements with exact formulas and interpretations.