How to Calculate Percent Change Between Two Numbers

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ProCalc.ai Editorial Team

Reviewed by Jerry Croteau, Founder & Editor

I was standing in the lumber aisle doing math on my phone and nothing was adding up.

I’d just grabbed a couple bundles of shingles, a roll of underlayment, and some random odds and ends, and the total on the receipt was higher than what I remembered from last month. Not “a little higher,” either. Like… enough higher that you start wondering if you accidentally bought the fancy version of something.

So I did what you do: I tried to calculate the percent change in my head, got tangled up, and then I realized I’ve watched a lot of people (smart people!) mix up “percent difference” and “percent change” and “percent off” like they’re all the same thing.

They’re not.

Percent change is basically: how much did it move compared to where it started?

And once you lock that in, the whole thing gets weirdly easy.

Percent change is “new vs old,” not “two random numbers”

The thing that trips people up is the “between two numbers” part. Sounds like either number could be the starting point, right? But percent change always has a direction. You’re going from an old value to a new value. If you swap them, you’ll get a different answer (same magnitude, opposite sign), and that’s not a math error — it’s you telling a different story.

So if your material cost went from 1,200 to 1,380, you’re asking: “How much did it increase relative to 1,200?” Not relative to the average, not relative to 1,380, not relative to your feelings.

And yeah, the sign matters. Positive means it went up. Negative means it dropped. If you’re looking at a discount, you actually want the negative number (even if your brain wants to call it “a positive discount”).

So why does everyone get this wrong? Because we say “between” like it’s symmetrical, but percent change isn’t symmetrical. It’s anchored to the starting number.

And if you want to sanity-check it: if New equals Old, the top becomes zero, and the percent change is zero. That’s exactly what you’d expect.

But if Old is zero… you can’t do it. Division by zero, whole thing blows up (in a boring math way, not a fun way).

A worked example (the one you’ll actually use)

Let’s do the “receipt got bigger” example because it’s real life and it’s where this shows up constantly.

You paid 1,200 last month. This month it’s 1,380. What’s the percent change?

1. Find the difference: New − Old = 1,380 − 1,200 = 180
2. Divide by the old value: 180 / 1,200 = 0.15
3. Convert to percent: 0.15 × 100 = 15

So it’s a 15 percent increase.

That’s a lot of shingles!

Now flip it. Say you caught a sale and the same stuff dropped from 1,380 down to 1,200. Same numbers, different direction:

• New − Old = 1,200 − 1,380 = −180
• −180 / 1,380 ≈ −0.1304
• × 100 ≈ −13.04

So that’s about a 13 percent decrease (give or take depending on how many decimals you keep). Notice it’s not 15 percent in reverse. That’s not a mistake — it’s because the “old” number changed.

I had no idea that mattered the first time someone pointed it out. I nodded like I understood. I didn’t.

Quick reference table (so you don’t have to re-derive it)

Here’s a little cheat sheet with common scenarios. Same formula every time, just different stories.

Scenario	Old	New	Percent change	What it means
Material cost went up	1,200	1,380	15%	Increase relative to last month
Discounted price	80	68	−15%	Price dropped by 15%
Split-bill tip bump	146	175	about 19.9%	Total increased after tip/tax
Weekly hours cut	45	36	−20%	Schedule reduced by a fifth

If you’re doing this a lot (and you probably are), you’ll eventually stop thinking about it as “percent change” and start thinking “difference over original.” Same thing, different words.

How I actually do this on a job: rough first, exact second

So here’s the honest workflow: I usually do a fast mental estimate first, and then I verify with a calculator because I don’t like being wrong in writing.

For a quick estimate, I round the old number into something friendly and see if the difference is “about 10 percent” or “more like 25 percent.” Like if something was 1,200 and it jumped 180, I know 10 percent of 1,200 is 120, and 20 percent is 240, so 180 is right in the middle. That’s 15 percent. No fancy math, just landmarks.

But if you’re sending a change order, or you’re comparing supplier quotes, or you’re trying to explain to a client why a line item moved… you want the exact percent, not the vibes.

And that’s where a calculator saves your brain for more important stuff.

Use the embedded one here if you just need the answer right now:

And if you’re bouncing between related math tasks (it happens more than you’d think), these are the ones I end up reaching for:

Fraction to decimal when a measurement or ratio shows up as a fraction and you want a clean number

Decimal to fraction for the opposite problem (and yes, it comes up)

if you’re comparing mixes, blends, or “this vs that” without a timeline

when you’re trying to smooth out a few prices or readings

if you’re dealing with very large or very tiny numbers and your eyes start crossing

Slope calculator for the “rise over run” moments (which… if you’ve ever framed anything, you know)

But percent change specifically? It’s still the same move: subtract, divide by old, multiply by 100.

FAQ (the stuff people ask me mid-calculation)

What if the percent change is negative — do I just ignore the minus sign?

Nope. The minus sign is the whole point. Negative means the new number is smaller than the old number. If you’re describing it in words, you can say “a 12 percent decrease” instead of “negative 12 percent,” but don’t drop the sign while you’re calculating or you’ll talk yourself into the wrong story.

Why isn’t the percent change the same going up and then back down?

Because the denominator changes.

Example: 100 up to 120 is (20/100)×100 = 20%. But 120 down to 100 is (−20/120)×100 ≈ −16.67%. Same 20 units, different “starting point,” different percent.

What do I do if the old number is 0?

• You can’t compute percent change with Old = 0 because you’d be dividing by zero.
• In practice, you either report the raw change (New − Old), or you pick a different baseline (like last non-zero period), or you just say “it went from 0 to 14” without forcing a percent onto it.

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