Introduction to Linear Interpolation Calculator:
Linear Interpolation Calculator with steps is an online tool that helps you to calculate interpolation linear questions in a couple of seconds. Our tool determines the estimating values between two points on a straight line.
The interpolation linear calculator is a great source of learning about linear interpolation methods for students, teachers, and researchers. As it simply the process of finding the middle value that is used in various fields like mathematics, physics, engineering, and computer graphics
What is Linear Interpolation?
Linear interpolation is a numerical analysis method used to find the estimated value from the given two endpoints on the graph. It is used to find the approximate values that are present between two known points at a plane.
It builds a linear relationship between the known points and the estimated point values at ends points along a straight line in a simple way.
What is Linear Interpolation Formula?
The linear interpolation formula is used to find the unknown value of y coordinates. The linear interpolation calculator uses this formula for its calculations which is given below,
$$ y \;=\; y_0 + \frac{(x - x_0) . (y_1 - y_0)}{(x_1 - x_0)} $$
Where:
- x0 and x1 are the known point value of x.
- y0 and y1 are the known point values of y.
- x is the estimated value of y.
- y is the interpolated value of y
How to Calculate Linear Interpolation?
The linear interpolation solver uses the linear interpolation method which makes it very easy to calculate the unknown points from the given plane with the help of the formula of linear interpolation.
Let's see how the linear interpolator calculator calculate interpolation linear with the help of an example with the solution. Suppose x = 6 along with Coordinates (7,5) and (8,9) find the y value with the linear interpolation formula.
Step 1:
First determine the given point as (x0, y0), (x1, y1),....(xn,yn) of a line. So, the given points are
$$ x_0 \;=\; 7 \;,y_0 \;=\; 5 $$
$$ x_1 \;=\; 8 \;,y_1 \;=\; 9 $$
Step 2:
Then check the x coordinate value for the estimated point through which you want to find the y coordinates value. In the example, the x coordinate value is 6 as x = 6.
Step 3:
Apply the interpolation formula, and put all the given values to find the linear interpolation point.
$$ y \;=\; y_0 + \frac{(x - x_0) . (y_1 - y_0)}{(x_1 . x_0)} $$
Step 4:
Simplify the values that you put on the formula to get the linear interpolation for y coordinates.
$$ y \;=\; 5 + (6-7) . \frac{(9-5)}{(8-7)} $$
$$ y \;=\; 5 + \frac{(-1).4}{(1)} $$
$$ y \;=\; 5 - 4 $$
$$ y \;=\; 1 $$
Step 5:
After calculation, you get the point of y coordinates because x coordinates are already present as (x,y) = (6,1). These are the interpolation points on a line.
The linear interpolation formula calculator uses the same above steps to solve the linear interpolation problems which you can also use to solve the complex problems.
How to Use the Linear Interpolation Calculator?
The interpolation linear calculator has an easy-to-use interface that enables you to use it to calculate linear interpolation questions. You must follow some simple steps to avoid trouble during the calculation process. These steps are:
- Enter the value of given points (x0, y0), (x1, y1),....(xn,yn) in the input box.
- Enter the value of the x coordinate in the input box.
- Recheck your input point value before hitting the calculate button to start the calculation process in the linear interpolation solver.
- Click on the “Calculate” button to get the desired result for the interpolation method problem. If you want to try out the linear interpolator calculator to check its accuracy in solution, then you must try out the load example to get clarity
- Click on the “Recalculate” button to get a new page for the determination of more values to get the estimated value.
Outcome from Interpolation Linear Calculator:
Linear interpolation Calculator with steps gives you the solution to a given value for interpolation points problem when you give input it. It provides you with solutions in the form of the y coordinate of a line in a step-wise process. It may contain:
- Result option provides you with a solution of interpolation points from the known values on a graph line.
- Possible steps option provides you with a solution where all calculation steps are included in detail.
Benefits of Using Linear Interpolation Solver:
Linear interpolation equation calculator gives you multiple benefits whenever you use it to calculate linear interpolation problems for an unknown value of y. These benefits are:
- Our linear interpolation equation formula calculator saves the time and effort that you consume during the lengthy calculation of the linear interpolation method.
- Interpolation linear calculator is a free-of-cost tool that provides you with a solution for linear interpolation method without paying.
- It is an adaptive tool that helps you to find the linear interpolation point from the given points in a plane
- You can use this linear interpolation formula calculator for practice so that you get in-depth knowledge about this concept.
- It is a trustworthy tool that provides you with exact solutions as per your input value whenever you use it to find the interpolation points problem.
- The linear interpolation Calculator with steps provides an accurate solution whenever you use it for the evaluation of linear interpolation questions.
