A percentage change calculator gives the shift between an earlier figure and a later one as a signed percent, worked out as (new - old) / old x 100. A mock score that goes from 142 to 167 is a change of plus 17.61 percent; an SGPA that slips from 8.4 to 7.9 is a change of minus 5.95 percent.
The sign is what sets this page apart from the separate increase and decrease pages. One formula covers both directions, which is why reports, result analyses and lab records use it when some rows go up and others go down. It is also the formula behind variance against a target and month on month change.
At a glance
Formula
(new - old) / old x 100Sign
Plus for a rise, minus for a fallVariance
(actual - planned) / planned x 100Rise example
142 to 167 = +17.61%Fall example
8.4 to 7.9 = minus 5.95%Old value zero
Percent change cannot be worked out
Percentage change = (New - Old) / Old x 100
Old is the earlier or reference figure and must not be zero. New is the later figure. A positive answer is a rise and a negative answer is a fall.
How the calculator above works
Put the earlier figure in the old box and the later one in the new box. The tool returns one signed percent, the raw change and a word saying rise or fall. Swap the boxes and the answer changes, because the base changes with them.
Whether you call it a change percentage calculator, a percentage of change calculator or a change in percentage calculator, this is the tool for any before and after pair.
- Identify the earlier figure (old) and the later figure (new).
- Subtract old from new and keep the sign.
- Divide by the old figure.
- Multiply by 100 and write the sign in front.
Percentage change calculator formula and why the old value is the base
Change = new - old
Percentage change = change / old x 100
A change always describes a journey from somewhere. The old value is where the journey started, so it is the yardstick. That is why 100 to 125 is plus 25 percent while 125 to 100 is minus 20 percent: the start point differs.
If the old value is zero, there is no percent change to report. Going from 0 to 12 is a rise of 12, but 12 / 0 has no answer. Say “up from zero” instead.
Worked examples, up and down
Mock score. Old 142, new 167. Change 25. 25 / 142 x 100 = plus 17.61 percent.
SGPA. Old 8.4, new 7.9. Change minus 0.5. minus 0.5 / 8.4 x 100 = minus 5.95 percent.
Pass rate of a class. Old 64 percent, new 72 percent. The rise is 8 percentage points. As a percentage change it is 8 / 64 x 100 = plus 12.5 percent.
Month on month (MoM). A college library logged 1,200 visits in one month and 1,380 the next. 180 / 1,200 x 100 = plus 15 percent MoM.
Variance percentage: actual against plan
Variance is percentage change with the plan as the old value. A department planned 400 hours of lab time for a term and used 452. Variance = (452 - 400) / 400 x 100 = plus 13 percent, meaning 13 percent over plan. If it had used 372 hours, the variance would be minus 7 percent, under plan.
A budget variance percentage calculator, a percentage variance calculator and a percentage of variance calculator all do exactly this. Write the planned or budgeted figure in the old box and the actual figure in the new box.
Change table for a starting value of 200
| New value | Change | Percentage change |
|---|---|---|
| 100 | minus 100 | minus 50% |
| 150 | minus 50 | minus 25% |
| 170 | minus 30 | minus 15% |
| 190 | minus 10 | minus 5% |
| 200 | 0 | 0% |
| 210 | plus 10 | plus 5% |
| 230 | plus 30 | plus 15% |
| 250 | plus 50 | plus 25% |
| 300 | plus 100 | plus 50% |
| 400 | plus 200 | plus 100% |
| 500 | plus 300 | plus 150% |
Notice that a fall can never go below minus 100 percent, but a rise has no upper limit.
Change over several periods
When a figure moves over several steps, find the overall change from the first value to the last, not by adding the step changes. A count that goes 500, then 550 (plus 10 percent), then 495 (minus 10 percent) ends at minus 1 percent overall, not zero.
To find the percentage rate of change per step without a rate of change calculator at hand, divide the last value by the first, take the nth root, where n is the count of steps, and subtract 1. From 500 to 605 over two steps: 605 / 500 = 1.21, root 1.1, so the rate is plus 10 percent per step.
Change versus difference, and slips to avoid
Change needs an order: old first, new second. If the pair has no natural order, for instance Batch 1 against Batch 2, the percentage difference calculator is built for that case: it measures the gap against the midpoint and drops the sign.
| Slip | Why it misleads | Better habit |
|---|---|---|
| Using the later figure as base | Shrinks every rise and enlarges every fall | Divide by the earlier figure |
| Dropping the sign | Readers cannot tell a gain from a loss | Write plus or minus every time |
| Adding step changes | Plus 10 and minus 10 is not zero | Compare first and last values |
| Reporting points as percent | 64% to 72% is 8 points, 12.5% change | Label which one you mean |
If you only ever deal with rises or only with falls, the increase and decrease pages word the answer for you. The main percentage calculator has all six modes.
Questions students ask
What is the percentage change formula?
Take new minus old, scale it against old and multiply by 100, keeping the sign. From 142 to 167 that gives plus 17.61 percent.
Can this tool act as a price change percentage calculator?
Use the old price as the base: (new price - old price) / old price x 100. A positive answer means the price went up and a negative one means it came down.
What does a MoM percentage change calculator show?
MoM means month on month. Use last month's figure as the old value and this month's figure as the new value. 1,200 to 1,380 is plus 15 percent MoM.
How is variance percentage calculated?
Take actual minus planned, divide by planned and multiply by 100. Using 452 hours against a plan of 400 is a variance of plus 13 percent.
Can percentage change be more than 100?
A rise can be any size: 200 to 500 is plus 150 percent. A fall stops at minus 100 percent, which means the value dropped to zero.
Why is my percentage change different from percentage difference?
Change uses the old value as its base and keeps a sign. Percentage difference is measured against the halfway point and carries no sign, so one pair can give two different figures.