How to find rate of change calculator

Your input: find the average rate of change of $$$f\left(x\right)=x^{2}$$$ on the interval $$$\left[1,3\right]$$$.

The average rate of change of $$$f\left(x\right)$$$ on the interval $$$[a,b]$$$ is $$$\frac{f(b)-f(a)}{b-a}$$$.

We have that $$$a=1$$$, $$$b=3$$$, $$$f\left(x\right)=x^{2}$$$.

Thus, $$$\frac{f(b)-f(a)}{b-a}=\frac{\color{red}{\left(3\right)}^{2}-\left(\color{red}{1}^{2}\right)}{3-\left(1\right)}=4$$$.

The Percentage Change Calculator (% change calculator) will quantify the change from one number to another and express the change as an increase or decrease. 

This is a % change calculator.  From 10 apples to 20 apples is a 100% increase (change) in the number of apples.

This calculator will be most commonly used when there is an “old” and “new” number or an “initial” and “final” value. A positive change is expressed as an increase amount of the percentage value while a negative change is expressed as a decrease amount of the absolute value of the percentage value.

You will generally use the percent change calculation when the order of the numbers does matter; you have starting and ending values or an "old number" and a "new number." When you are just comparing 2 numbers you may want to use the percent difference formula and calculation.

Related calculations can be done with Percentage Calculator and conversions can be solved with Decimal to Percent, Percent to Decimal, Fraction to Percent, or Percent to Fraction.

Percentage Change Formula

Percentage change equals the change in value divided by the absolute value of the original value, multiplied by 100.

\( \text{Percentage Change} = \dfrac{\Delta V}{|V_1|} \times 100 \)

\( = \dfrac{(V_2-V_1)}{|V_1|} \times 100 \)

For example one, how to calculate the percentage change:

What is the percentage change expressed as an increase or decrease for 3.50 to 2.625?

Let V1 = 3.50 and V2 = 2.625 and plug numbers into our percentage change formula

\( \dfrac{(V_2-V_1)}{|V_1|} \times 100 \)

\( = \dfrac{(2.625 - 3.50)}{|3.50|} \times 100 \)

\( = \dfrac{-0.875}{3.50} \times 100 \)

\( = -0.25 \times 100 = -25\% \; \text{change} \)

Saying a -25% change is equivalent to stating a 25% decrease.

Note that if we let V1 = 2.625 and V2 = 3.50 we would get a 33.3333% increase. This is because these percentages refer to different amounts: 25% of 3.50 versus 33.3333% of 2.625.

As a second example let's look at a change that includes negative numbers, where taking the absolute value of V1 in the denominator makes a difference.

What is the percentage change expressed as an increase or decrease for -25 to 25?

Let V1 = -25 and V2 = 25 and plug numbers into our formula:

\( = \dfrac{(25 - -25)}{|-25|} \times 100 \)

\( = \dfrac{50}{25} \times 100 \)

\( = 2 \times 100 = 200\% \; \text{change} \)

Saying a 200% change is equivalent to stating a 200% increase.

As a third and final example let's look at another change that includes negative numbers, where taking the absolute value of V1 in the denominator makes a difference.

What is the change expressed as an increase or decrease for -25 to -50?

Let V1 = -25 and V2 = -50 and plug numbers into our formula:

\( = \dfrac{(-50 - -25)}{|-25|} \times 100 \)

\( = \dfrac{-25}{25} \times 100 \)

\( = -1 \times 100 = -100\% \; \text{change} \)

Saying a -100% change is equivalent to stating a 100% decrease.

References

Wikipedia contributors. "Percent difference: percent change" Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, last visited 18 Feb. 2011.

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Enter the location of two coordinate points along a line into the calculator to determine the rate of change of that line.

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Rate of Change Formula

The following formula is used to calculate a rate of change.

Rate of Change = (y₂ – y₁) / (x₂ – x₁)
y₂ = y coordinate of point 2
y₁ = y coordinate of point 1
x₂ = x coordinate of point 2
x₁ = x coordinate of point 1

Rate of Change Definition

The rate of change of a line is often referred to as the slope, or rise over run. It’s a measure of how quickly a line is changing in the y-direction with every step in the x-direction.

This can also be done using a similar formula, but substituting x and y in the formula. This results in the rate of change of x with respect to y, or run over rise.

How do you calculate the rate of change?

How do you find the rate of change between two values?