Reverse Percentage Calculator

Original Value

Decrease Rate %

New Value

170.00

A 15.00% decrease on 200.00 gives 170.00.

Formula

New = Original × (1 − Rate ÷ 100)

A reverse percentage calculation finds a missing original value from a known result and a known rate, the mirror image of the usual "what's the decrease" question. Given a reduced value and the rate it fell by, this tool recovers what it started at; give it an original value and a rate instead, and it runs forward to find the result.

This is a deeper, dedicated version of the reverse calculation the homepage introduces briefly in its own worked example, the same idea, with both directions built in and the tricky edge cases covered in full below.

How to Recover an Original Value

The direction most people actually need: working backward from a reduced value to what it used to be.

Express the rate as a decimal multiplier
Divide the new value by that multiplier
Check by applying the forward formula
Watch the rate as it approaches 100%

Common Mistake

Adding the percentage back onto the reduced value instead of dividing. A value that fell 20% to reach 80 did not start at 80 + 20% of 80 = 96, it started at 80 ÷ 0.80 = 100. The 20% was calculated against the original 100, not the reduced 80, so adding it back to the wrong base always undershoots. As covered on the homepage's jacket example, dividing is the only operation that correctly undoes a percentage decrease.

Reverse Percentage Examples

A salary before a pay cut, and an inventory count before a reported decline.

Example 1, Salary after a 12% pay cut is $61,600. What was it before?

$70,000

Identify the values New = $61,600, Rate = 12%
Express the rate as a multiplier 1 − 12 ÷ 100 = 0.88
Divide the new value by the multiplier 61,600 ÷ 0.88 = $70,000
Check 70,000 × 0.88 = 61,600 ✓

A salary cut 12% to $61,600 was $70,000 beforehand, dividing by 0.88 undoes the cut exactly, while adding 12% of $61,600 back would have wrongly suggested $68,992.

Example 2, Inventory fell 35% to 2,600 units. What was the original count?

4,000 units

Identify the values New = 2,600 units, Rate = 35%
Express the rate as a multiplier 1 − 35 ÷ 100 = 0.65
Divide the new value by the multiplier 2,600 ÷ 0.65 = 4,000 units
Check 4,000 × 0.65 = 2,600 ✓

A reported 35% inventory decline to 2,600 units means the count started at 4,000, useful for reconstructing a prior period's figures when only the change and the result were reported.

Relationship to Percentage Decrease

Every reverse calculation on this page starts from the same formula as the homepage's percentage decrease calculator, solved for a different variable. The forward direction, Original × (1 − Rate ÷ 100) = New, is exactly what the homepage computes when it reports a decrease; this page rearranges that same equation to solve for Original when New and Rate are known instead. For the full algebraic derivation of both rearrangements, see the formula deep-dive; for how this concept connects to everything else on the site, see the complete guide.

Frequently Asked Questions

What happens to the reverse formula as the rate approaches 100%?

The multiplier (1 − rate ÷ 100) shrinks toward zero, so the recovered original value grows without bound, a new value of 10 after a 99% decrease implies an original of 1,000; after a 99.9% decrease, an original of 10,000. The closer the rate gets to 100%, the more sensitive the recovered original becomes to small errors in the rate.

Why can't I just add the percentage back to the reduced value?

Because that percentage was calculated against the original value, not the reduced one, adding it back to the smaller number takes a percentage of the wrong base. As covered on the homepage's worked example, this exact mistake produces a smaller, wrong answer every time; the fix is always to divide by (1 − rate ÷ 100), never to add the rate back.

Can I recover the original value if I only know the amount decreased, not the rate?

Yes, but you need the new value too: Original = New + Amount Decreased. The rate-based reverse formula on this page is for the more common case where you know the rate and the resulting value, but not the original.

How do I reverse a percentage increase instead of a decrease?

Divide by (1 + rate ÷ 100) instead of (1 − rate ÷ 100). A value that grew 20% to reach 300 started at 300 ÷ 1.20 = 250. See the percentage increase calculator for the forward direction.

What if the rate I enter is negative?

A negative rate in the forward direction (Original × (1 − rate ÷ 100)) produces growth instead of decline, since subtracting a negative rate is the same as adding a positive one, the formula still works, it just describes an increase rather than a decrease.

Is there a reverse formula for percentage points instead of percentage decrease?

Not in the same sense, percentage points are found by plain subtraction, and reversing that just means adding the point difference back to the other percentage. There's no multiplier or division involved, which is exactly why confusing percentage points with percentage decrease leads people to the “just add it back” mistake this page warns about.

How is this used to recover an original salary before a pay cut?

If you know your reduced salary and the percentage it was cut by, divide the reduced salary by (1 − rate ÷ 100) to recover what you were earning before. See the worked example below for a $70,000 salary reduced 12%.

Can rounding in a reported rate throw off the recovered original value significantly?

Yes, especially as the rate climbs. A rate reported as "about 90%" instead of an exact 90.0% can shift the recovered original by a meaningful amount, since you're dividing by a small number that rounding affects proportionally more.

What happens with the reverse formula for rates above 100%?

The multiplier (1 − rate ÷ 100) becomes negative, which flips the sign of the recovered original value, mathematically consistent, but it signals the input data describes something unusual (like a value crossing through zero) rather than an ordinary decrease, and is worth double-checking.

How do I reverse a series of multiple sequential decreases?

Divide by each multiplier in reverse order, if a value fell 10% and then 15%, recover it by dividing the final value by 0.85, then dividing that result by 0.90. Multiplying the two rates together and dividing once will give the wrong answer, the same way stacking discounts doesn't add.