# Rate of Change Calculator

The free rate of change calculator provides an estimate of slope change given input coordinates. With STUDYQUERIES’s online rate of change calculator tool, rates of change can be calculated in less than a minute and the result is displayed instantly.

## How to Use the Rate of Change Calculator?

You can use the rate of change calculator by following these steps:

• Step 1: The first step is to enter the X and Y coordinates in the appropriate fields. In other words, (x1, y1) and (x2, y2)
• Step 2: After clicking the button “calculate Rate of Change” the result will be shown
• Step 3: You will see the result in the output field

## What Is the Rate of Change?

According to this definition, the rate of change refers to the degree of change between two quantities. The rate of change can be summed up in simple terms as the difference in one item divided by the difference in another. Let’s learn more about the rate of change formula by looking at a few examples.

### What Is the Rate of Change Formula?

The formula for the rate of change describes the relationship between one quantity and another quantity. To find out the rate of change from coordinates of y to coordinates of x, take the following formula:

$$Δy/ Δx = (y2 – y1 )/ (x2 – x1 )$$

For a linear function, the rate of change m is represented in the slope-intercept form for a line: $$y = mx+b$$ whereas the rate of change of functions is otherwise defined as,

$$(f(b)-f(a))/ (b-a)$$

### Rate of Change Formulas

Formula 1: Here is the basic formula for calculating the change in rate:

Rate of change = (Change in quantity 1) / (Change in quantity 2)

Formula 2: Algebraic formulas for change rate

$$Δy/ Δx = (y2 – y1 )/ (x2 – x1 )$$

Formula 3: Rate of change of functions: $$(f(b)-f(a))/ (b-a)$$

### Applications of Rate of Change Formula

The rate of change tells us how something changes over time.

• Distance is driven by car in a certain amount of time.
• An electrical circuit’s current increases by some amperes for every volt of increased voltage.
• Furthermore, it is a crucial concept in finance as well. By understanding its principles, investors can spot trending securities.
• Work done per unit of time.
• Work done and the number of people required to complete it

For a better understanding of the rate of change formula, let us look at a few examples.

Example 1: Find the average rate of change of f(x)=x² on the interval [1,3].

The average rate of change of f(x) on the interval [a,b] is

$$(f(b)-f(a))/ (b-a)$$ We have that a = 1, b = 3, f(x) = x²

Thus, $$(f(b)-f(a))/ (b-a)$$

= $$(3)²−(1)²/ (3-1)$$ = 4.

Answer: the average rate of change is 4.

Example 2: Find the rate of change if the coordinates are (5, 2) and (7, 8).

Solution:

Rate of change or slope = change in y/change in x

= (y– y1) / (x2 – x1)

= (8 – 2) / (7 – 5)

= 6 / 2

= 3

The rate of change is positive. Thus, the graph will slant upwards.

Example 3: Find the rate of change if the coordinates are (32.5, 15) and (30, 25.7).

Solution:

Rate of change or slope = change in y/change in x

= (y– y1) / (x2 – x1)

= (25.7 – 15) / (30 – 32.5)

= 10.7/ (-2.5)

= -4.28

The rate of change is negative. Thus, the graph will slant downwards.

## Frequently Asked Questions on Rate of Change Calculator

### How do you calculate the rate of change?

Calculate the difference (increase) between the two numbers you are comparing. Divide the increase by the original number and multiply the result by 100. % increase = Increase ÷ Original Number × 100.

### What is the rate of change?

The rate of change is defined as the relationship between one quantity and another. A variable that is independent is x, and a variable that is dependent is y. This means that change in x/change in y represents the rate of change. Rates of change can be negative or positive.

### What is the formula for rate?

Rates of speed and distance and the use of time and distance are often involved in everyday problems. Cross products and proportions can be used to solve these problems. It’s easier to use a simple formula: rate equals distance divided by time: r = d/t.

### What is the rate of change Example?

Rat population grows by 40 rats per week. Driving 68 miles per hour (distance traveled changes by 68 miles per hour as time passes) Driving 27 miles per gallon of gasoline (distance traveled changes by 27 miles for every gallon).

### What is the rate of change slope?

It is a comparison between the change in the values of the x variables and the change in the values of the y variables. Rates of change are linear and constant when the line slope is equal to the rate of change. Lines may have a slope that is positive, negative, zero, or undefined.

### What is the rate of change of momentum equal to?

A particle’s mass is multiplied by its velocity to find the particle’s momentum. A vector quantity has both magnitude and direction, which is why it is called momentum. In Isaac Newton’s second law of motion, the particle’s momentum changes with time at a rate equal to its force.

### What is the percent of change from 8 to 6?

The percent decrease from 8 to 6 is 25 percent! Explanation: What does 25 percent or 25% mean? Percent (%) is an abbreviation for the Latin “per centum”, which means per hundred or for every hundred. So, 25% means 25 out of every 100.

### What is a positive change rate?

A positive rate of change means that the quantity you are measuring is increasing over time, and a negative rate of change means that it is decreasing over time.

### What’s the constant rate of change?

A linear function y = f(x) has a slope equal to its rate of change with respect to the variable x. In Definition 2, if both x and f have units, then the units of the rate of change are those of f divided by those of x.