Relative Change Calculator — Change Relative to the Initial Value

Our relative change calculator is here to help you calculate the relative change between a variable's initial and final values. It also calculates the percentage of relative change.

In this article, we shall learn what relative change is and apply the relative change formula to some example problems to help you understand this concept better.

🙋 If you specifically wish to calculate the relative increase or decrease of a quantity, we recommend a dedicated percentage increase or percentage decrease calculator.

What is relative change?

Relative change is a quantitative term that measures the change or difference in a variable relative to a reference or initial value. It helps compare two quantities while considering their "size".

The formula for relative change is:

Relative Change(xi, xf) = (xf − xi) / |xi|

where:

• xi — The initial value of a variable; and
• xf — The final value of the same variable.

As you can see, we calculate the relative change by subtracting the initial value from the final value and then dividing the answer by the absolute value of the initial number. The division by the initial value ensures that:

• The relative change is a unitless number; and
• The relative change between two quantities remains constant irrespective of the units used to measure the quantities.

For example, if the initial value is 4 km and the final value is 6 km, the relative change is (6 − 4) / 4 = 0.5. If we use meters instead of kilometers to measure the distance, the initial value would be 4000 m, and the final value would be 6000 m. Again, the relative change is (6000 − 4000) / 4000 = 0.5.

How do you calculate relative change?

Follow these three steps to find the relative change by hand:

1. Determine the initial value (xi) — the reference amount you start from. It must be non-zero;
2. Pick the final value (xf) — the amount you end with; and
3. Subtract the initial value from the final value, then divide by the absolute value of the initial value: (xf − xi) / |xi|.

Multiplying the relative change by 100 gives you the relative change percentage:

Relative Change (%) = (xf − xi) / |xi| × 100%

Example problems

Let's put the relative change formula to work:

• An increase: A stock rises from $50 to $65. The relative change is (65 − 50) / |50| = 0.3, or +30%.
• A decrease: A car's value drops from 20,000 ₽ to 17,000 ₽. The relative change is (17,000 − 20,000) / |20,000| = −0.15, or −15%.
• A negative reference: A temperature moves from −4 °C to −1 °C. The relative change is (−1 − (−4)) / |−4| = 3 / 4 = 0.75, or +75%. Note the initial value's sign is removed only in the denominator.

Using this relative change calculator

1. Select the unit type — Plain Number, Currency, Imperial (US), or Metric measurement.
2. If using Currency, pick your preferred currency from the list (USD, RUB, EUR, GBP, JPY, and 20+ more).
3. If using Imperial or Metric, choose the specific unit (inches, feet, kilograms, meters, etc.).
4. Enter the initial value (xi) — the reference number you start with. It cannot be zero.
5. Enter the final value (xf) — the number you end with. A live preview shows the relative change and percentage as you type.
6. Click Calculate — the calculator shows the relative change (xf − xi) / |xi| as a unitless ratio, the relative change percentage, its direction (increase, decrease, or no change), and a step-by-step solution.

FAQs

What is the relative change formula?

The relative change between an initial value xi and a final value xf is (xf − xi) / |xi|. It divides the difference by the absolute value of the initial value, producing a unitless ratio. Multiply by 100 to express it as a percentage.

Why is relative change unitless?

Because you divide a change measured in some units (say, kilometers) by an initial value measured in the same units, the units cancel out. This is what lets you compare relative changes across quantities of different sizes or measured in different units.

Can relative change be negative?

Yes. When the final value is smaller than the initial value, the numerator xf − xi is negative, so the relative change is negative — indicating a decrease. For example, going from 10 to 8 gives (8 − 10) / |10| = −0.2, or −20%.

Why can't the initial value be zero?

The relative change formula divides by the absolute value of the initial value, |xi|. Division by zero is undefined, so relative change has no meaning when the reference value is zero.

What is the difference between relative change and absolute change?

Absolute change is the raw numerical difference xf − xi in the original units. Relative change expresses that difference relative to the initial value, (xf − xi) / |xi|, giving a unitless ratio (or percentage). Absolute change answers "by how many units?"; relative change answers "by what proportion?".