Find the signed percent change between any two values — up or down, with direction labeled. Free, fast, and mobile-friendly.
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Did it go up or down — and by how much, relatively? The percentage change is the single number that answers both: its sign gives the direction, its size the magnitude. From 120 to 150 is +25%; from 150 to 120 is −20%. Our free Percentage Change Calculator computes the signed percent change between any old and new values, labeling the direction in plain words.
The formula is the workhorse of quantitative life: (new − old) / |old| × 100. The numerator’s sign carries the direction — positive for growth, negative for decline — while dividing by the old value’s magnitude normalizes the change so that $10 on $100 and $100 on $1,000 both read as 10%.
Unlike the increase-only and decrease-only framings, percentage change handles both directions in one signed number, which is why spreadsheets, dashboards, and financial reports prefer it. Enter any two values (old cannot be zero) and get the change with its full derivation.
Percentage change is signed because change itself is directional. The formula’s numerator (new − old) is positive when the value grew and negative when it shrank; the denominator |old| is always positive, so the quotient’s sign faithfully reports the direction. +25% and −25% are not just different sizes — they are opposite stories.
Using |old| (absolute value) in the denominator is a deliberate choice for handling negative baselines. From −100 to −50, the value improved by 50 in absolute terms; dividing by |−100| = 100 gives +50%, matching the intuition of “half the loss recovered.” Dividing by −100 instead would flip the sign confusingly.
The asymmetry of reversals is the deepest lesson here. A +25% move followed by −25% does not return to start: 120 → 150 → 112.5. Each percent applies to its own baseline. To undo a +p% change requires a −(100p/(100+p))% change — for p=25, that is −20%. The calculator’s signed output keeps this visible.
Zero baselines break the formula — division by zero is undefined, and “growth from nothing” has no percent. Negative-to-positive crossings (e.g., −50 to +50) produce percents over 100% that are technically correct but often misleading; report absolute changes alongside them.
Percent change = ((New − Old) / |Old|) × 100%
Positive = increase, negative = decrease. Old value must not be zero.
From 120 to 150: change = 30; 30 ÷ 120 = 0.25 → +25%. Check: 120 × 1.25 = 150 ✓.
From 200 to 150: change = −50; −50 ÷ 200 = −0.25 → −25%, a 25% decrease.
From 75 to 75: change = 0 → 0%. The calculator reports “no change” rather than a bare zero.
From −100 to −50: change = +50; 50 ÷ |−100| = 0.5 → +50%. The loss halved — correctly reported as a positive change.
Stock dashboards show signed changes: $120 → $150 prints +25% in green; the reverse prints −20% in red. Traders read direction and magnitude in one glance — the sign does half the work.
Business KPIs track month-over-month change: revenue from $200k to $230k is +15%. A negative print (−5%) triggers investigation. Executives scan columns of signed percents because the sign instantly separates wins from losses.
In health, weight from 180 lb to 171 lb is (171−180)/180 = −5% — a 5% decrease. Apps report the signed value so users see progress direction without interpreting raw pounds.
Modern dashboards are built on signed percent change: every KPI tile shows a value and a green/red percent vs the prior period. The sign does half the communication — green +12% needs no sentence. But dashboard designers must choose baselines carefully: month-over-month, year-over-year, and vs-budget tell different stories from the same current number. The percent is only as honest as its baseline.
Negative baselines are the classic dashboard trap. A profit line going from −$50k to −$10k improved by $40k; the formula gives (+40)/|−50| = +80% — correctly green. But from −$10k to +$10k: change +20k over |−10k| = +200%, a huge percent for crossing zero. Analysts often suppress percents near zero-crossings and show absolutes instead.
Logarithmic thinking offers an alternative: the log change ln(new/old) is symmetric (−ln for reversals) and additive over periods. Quants use log returns for exactly this reason. But for general audiences, the signed percent remains standard — with its asymmetries disclosed, as this page does.
Change 15; 15 ÷ 50 = 0.3 → +30%. Reconstruct: 50 × 1.30 = 65 ✓. The growth factor (1 + p/100) always rebuilds the new value — the universal check.
Change −27; −27 ÷ 90 = −0.3 → −30%, a 30% decrease. Reconstruct: 90 × 0.70 = 63 ✓. The retention factor (1 − 0.30) mirrors the growth factor.
Signed percent change is the native language of economics reporting: GDP +2.1%, inflation +3.4%, unemployment -0.2 points (note: points, not percent). Journalists must keep the sign and the baseline straight – “unemployment fell 0.2 percentage points to 4.1%” is exact; “fell 0.2%” would mean something 20x smaller. Economic literacy is largely signed-percent literacy.
Revenue goes $1.2M -> $1.5M. Change: 0.3/1.2 = 0.25 -> +25%. Verify: 1.2 x 1.25 = 1.5.
Temperature drops 68F -> 51F. Change: -17/68 = -0.25 -> -25%, a 25% decrease. (Percent of Fahrenheit readings is physically informal, but arithmetically fine.)
A population grows 12,000 -> 12,600. Change: 600/12,000 = 0.05 -> +5%.
A crypto asset falls $400 -> $300 -> $400. Leg 1: -100/400 = -25%. Leg 2: +100/300 = +33.3%. The round trip needs +33.3% to undo -25%.
A SaaS dashboard shows monthly recurring revenue: $840K -> $798K. Percent change: (798-840)/840 = -5%. The tile renders red with “-5% MoM.” The CEO drills in: the $42K drop came from two enterprise churns ($50K) offset by $8K in expansions. The signed percent told her direction and magnitude in one glance; the drill-down gave the story.
Next month: $798K -> $838K, a +5.03% change. The CEO notes the asymmetry aloud: “-5% then +5% didn’t recover us – we’re at $838K, not $840K.” The dashboard team adds a “vs. two months ago” tile: (838-840)/840 = -0.24%. The signed-change framing made the incomplete recovery visible; a less careful team would have celebrated “+5%” and missed it.
Dashboard literacy is signed-percent literacy: read the sign, check the baseline, distrust round trips.
The dashboard team fix – adding the two-month comparison – reflects a general principle: always anchor percents to a meaningful baseline. Month-over-month change is volatile; quarter-over-quarter is stable; year-over-year removes seasonality. The same current value tells three different stories against three baselines, and honest reporting shows the relevant ones. The signed percent is only as truthful as its denominator.
A final practical note: when reporting change to others, pair the signed percent with the absolute change. “+5% (+$40K)” is unambiguous; “+5%” alone invites baseline confusion. The best dashboards show both – the percent for the glance, the absolute for the grounding. Communication, like computation, benefits from redundancy.
Teams that track change well also track the base: a “+5%” on a $10K base and a “+5%” on a $1M base are different amounts of money. The percent normalizes; the absolute grounds. Always know both.
The Percentage Change Calculator computes ((new−old)/|old|)×100% with sign indicating direction (positive = increase, negative = decrease). It rejects zero old values, labels direction in words, and shows the change and division steps.
(New − Old) ÷ |Old| × 100. From 120 to 150: (30/120)×100 = +25%. The sign is the direction — never drop it.
−25%. Change −50 ÷ 200 = −0.25 → a 25% decrease. Negative means decrease; read the magnitude.
Percent change is directional (baseline = old value); percent difference is symmetric (baseline = average). Use change for time series, difference for peer comparison. Time series need baselines; peer comparison needs averages.
Yes — negatives mean decrease. −20% is a 20% decline. The sign is the direction. Signed values preserve direction information.
No change: new equals old. Zero change is informative, not empty.
So negative baselines give intuitive signs: −100 → −50 is +50% (loss halved), not −50%. Absolute baselines keep negative-start signs intuitive.
With a 20% decrease: 120 → 150 → 120. Undoing +p% needs −100p/(100+p)%. The reversal needs −100p/(100+p)%.
Undefined — division by zero. Describe it as an absolute rise of 50 from zero instead. Zero baselines have no percent — use absolutes.
Cite this page as: Percentage Change Calculator. Sigma Calculator. Retrieved October 9, 2026, from https://sigmacalculator.net/math-calculators/percentage-change-calculator/
Last updated: October 9, 2026