Percentage Decrease Formula

Original Value

New Value

Percent Decrease

30.00%

Amount Decreased

27.00

90.00 fell to 63.00, a decrease of 30.00%.

Formula

Percent Decrease = ((Original − New) ÷ |Original|) × 100

The homepage calculator covers what this formula is and how to use it. This page goes further: the notation differences you'll see across other sources, the algebra behind solving for a different variable, why stacking decreases doesn't add the way intuition suggests, and a few more spreadsheet patterns beyond the basic formula.

Notation Variants Used Across Sources

The same formula appears under at least three naming conventions, depending on where you learned it:

Starting / Final Value: Common in general math and business writing, "Starting Value" and "Final Value" mean exactly what this site calls "Original" and "New."
Initial / New Value: Common in science and engineering texts, "Initial Value" is identical to "Original Value" in every formula on this site.
V1 / V2: Common in statistics, a deliberately generic notation with no implied real-world context, where V1 plays the role of Original and V2 plays the role of New.

All three describe the identical calculation. If a formula you find elsewhere looks different from this site's, check the variable names before assuming the math itself disagrees.

A fourth convention worth recognizing: some finance and statistics sources write the formula using P₀ (initial period) and P₁ (subsequent period) subscripts instead of named variables, which is common in time-series contexts where there may eventually be a P₂, P₃, and so on. It's the identical two-value formula on this page, just indexed for a sequence rather than named for a single comparison.

Algebraic Rearrangements

The base formula solves for the rate. Rearranged, it can just as easily solve for the new value or the original value instead , the two directions the reverse percentage calculator handles as a dedicated tool.

Solving for the New Value

Given Original and Rate

New = Original × (1 − Rate ÷ 100)

Example: an original value of 440 with an 15% rate gives New = 440 × 0.85 = 374.

Solving for the Original Value

Given New and Rate

Original = New ÷ (1 − Rate ÷ 100)

Example: a new value of 374 that resulted from a 15% decrease gives Original = 374 ÷ 0.85 = 440, the same pair of numbers, worked in the other direction. The reverse percentage calculator handles both directions interactively, including the edge case where this rearrangement breaks down entirely at a 100% rate.

Solving for the Rate

Given Original and New

Rate = ((Original − New) ÷ |Original|) × 100

This is the base formula itself, solving for the rate is what the homepage calculator does whenever both the original and new value are already known. It's listed here alongside the other two rearrangements to make clear that all three are the same equation, just isolated for a different unknown.

Compounding Decreases

Two successive 10% decreases are not a 20% decrease, a mistake intuitive enough that it's worth proving with real numbers. Starting from 400:

After the first 10% decrease400 × 0.90 = 360
After the second 10% decrease360 × 0.90 = 324
Total decrease from 400 to 324(400 − 324) ÷ 400 × 100 = 19.00%

The combined result is 19%, not 20%, because the second 10% is calculated against the already-reduced 360, not the original 400. This is the identical reasoning behind why stacked discounts don't add either. It's the same compounding formula applied to pricing.

Add a third 10% decrease and the gap widens further: 324 × 0.90 = 291.60, a combined decrease of (400 − 291.60) ÷ 400 × 100 = 27.10%, not the 30% naive addition would suggest, and further from it than the two-decrease case was. Each additional decrease compounds on a smaller base, so the shortfall from simple addition grows with every step rather than staying fixed.

Excel and Sheets, Reprised

The homepage covers the basic single-cell formula. Two more patterns worth knowing:

An Array Formula for a Whole Column

Array formula (Ctrl+Shift+Enter in older Excel, or native in Sheets/365)

=ARRAYFORMULA((A2:A100-B2:B100)/ABS(A2:A100)*100)

This computes the percentage decrease for every row from 2 to 100 in one formula, instead of writing and dragging the same formula down the column manually.

Wrapping Blank Cells Safely

Guard against blank or zero original values

=IFERROR((A2-B2)/ABS(A2)*100, "")

This returns a blank cell instead of a #DIV/0! error whenever the original value in column A is empty or zero, which keeps a summary report clean when pulling from a data source that isn't fully filled in yet.

Relationship to Percentage Decrease

Everything on this page is the same percentage decrease formula the homepage introduces, examined from every algebraic angle: renamed variables, solved for a different unknown, chained across multiple periods, and expressed in spreadsheet syntax. There is exactly one formula underneath all of it.

Frequently Asked Questions

What's the difference between "Starting Value" and "Original Value" in different sources?

Nothing, they're the same variable under different names. Textbooks, spreadsheets, and finance sites all describe the same quantity (the figure a change is measured against) using whichever term fits their context, and this site uses "Original" for consistency across every calculator.

Why do some textbooks use V1/V2 instead of Original/New?

V1/V2 notation is common in statistics and general algebra texts because it avoids implying a specific real-world context (money, population, and so on). It's the same formula, just with placeholder variable names instead of descriptive ones.

How do I solve for the rate if I only have the formula written as New = Original × multiplier?

The multiplier already contains the rate: multiplier = 1 − Rate ÷ 100. Rearranged, Rate = (1 − multiplier) × 100. A multiplier of 0.82 corresponds to an 18% decrease.

Is there a single formula for compounding multiple decreases?

Yes, multiply all the individual multipliers together, then convert the combined multiplier back to a percentage: Combined Rate = (1 − (m₁ × m₂ × m₃ × …)) × 100. This is the only mathematically correct way to combine sequential percentage decreases; adding the individual rates gives a different, larger number.

Why is an array formula faster than dragging the same formula down a column in a spreadsheet?

A single array formula is evaluated once by the spreadsheet engine and spread across the range, while a dragged formula is recalculated as N separate cell formulas, for small sheets the difference is invisible, but on very large datasets the array version avoids redundant recalculation overhead.

What does IFERROR actually catch in this formula?

It catches the #DIV/0! error that Excel and Google Sheets raise whenever the original value is 0, since the formula divides by it. Wrapping the formula in IFERROR lets you substitute a blank cell or a custom message instead of an error code spreading across a report.

Can this formula be written for many periods using summation notation?

Compounding across n periods is usually written as a product, not a sum: Final = Original × ∏(1 − rᵢ ÷ 100) for i = 1 to n, where each rᵢ is that period's rate. It's a product because each period's decrease multiplies the result of the previous one, rather than adding to it.

Is the percentage decrease formula identical in every spreadsheet program?

The arithmetic is universal, but function names can differ slightly, ABS() is standard in Excel, Google Sheets, and most others, though some regional spreadsheet locales translate function names into the interface language while keeping the underlying formula identical.

How do I verify a percentage decrease formula is implemented correctly in code?

Test it against at least three cases: a normal decrease (original > new, positive result), an increase (original < new, negative result), and a zero original value (should raise an error or return null, never NaN silently). If all three behave correctly, the absolute value and sign handling are almost certainly right.

Why do two different sources sometimes report slightly different percentage decrease formulas?

Usually because one source omits the absolute value in the denominator, which only produces a different answer when the original value is negative, for positive original values, every correctly written version of the formula agrees exactly.