Linear Interpolation Calculator & Formula

    Use this linear interpolation calculator to search for points on a given line. You can determine the value either using the slope intercept form or by using two coordinates. In this article, you’ll learn how to use the calculator and other information regarding linear interpolation. Read on to learn more.

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    How to use the linear interpolation calculator?

    This very simple interpolation calculator serves as a convenient tool for when you need to find the values you need. Instead of solving manually using the linear interpolation formula, this calculator is much easier and it provides you with the results instantly. Here are the steps to follow for this online tool:

    • First, enter the values of x1 and y1.
    • Then enter the values of x2 and y2.
    • Finally, enter the values of x3 and y3.
    • After entering all of the required values, the linear interpolation calculator automatically generates for you the values of m and b given the formula slope intercept form:

    y = mx + b.

    • Under these values, you can also see the whole formula with the values already substituted into it. This gives you a good reference for how you can write down the formula along with the required values.

    What is interpolation method?

    The interpolation method refers to a statistical method by which you use related known values to come up with an estimation for an unknown potential yield or price of a given security. You can achieve this method by using other known values related to it and which come in sequence with the unknown values.

    At its very root, interpolation is a simple concept in mathematics. If you notice a trend across a collection of data points that’s generally consistent, you can come up with a reasonable estimation of the value of the data set even at points which you haven’t calculated yet. Of course, this is only an estimate at best. The problem with interpolators is that you can never have full confidence in their estimations.

    There are different kinds of interpolation you can work with. These include polynomial interpolation, piecewise constant interpolation, and linear interpolation. Among all of these methods, the most common and easiest to do is a linear interpolation. For this method, you can either use a linear interpolation equation or a linear interpolation calculator which is much more convenient.

    This is very useful when you’re trying to come up with an estimation of the value of an interest rate or security for a specific point at which there’s no available data. You shouldn’t confuse interpolation with extrapolation. The latter refers to a method by which you can come up with an estimation for a data point outside of the known data range.

    Often, charts which represent the history of stocks are widely interpolated. They use linear regression to create the curves which represent an approximation of a security’s price variations. Even if a chart which measures a stock over the course of a year includes data points for each day, it’s impossible to say with full confidence where the stock would have gotten valued at a given point in time.

    Although this definition seems confusing at first, the actual concept of interpolation is relatively simple. Human civilizations have used interpolation for centuries, particularly by the early Mesopotamian astronomers as well as the ones in Asia Minor as they attempted to fill in the gaps.

    Although several factors affect the movements of the planetary bodies, they’re still better suited to interpolations lack of precision compared to the fluctuations of stocks which are highly unpredictable. Nonetheless, with the huge amount of data involved in the analysis of securities, it’s quite difficult to avoid interpolations in terms of price movements.

    What is the linear interpolation formula?

    Although using this linear interpolation calculator is easier, you may still want to perform the calculation by hand using the linear interpolation equation. For this, try to imagine that you need to measure the dependence between how much flour you need and how many cookies you want to bake.

    The first time you baked a batch of cookies, you used 200 grams of flour and ended up with 15 cookies. The second time you baked a batch of cookies, you used 300 grams of flour and ended up with 20 cookies. Now, you would like to know the number of cookies you would get when you use 250 grams of flour.

    Let’s assume that this situation has a linear relationship so you can solve for the linear interpolation. If you need to solve for a value beyond the range you’ve already tested, this refers to extrapolation. But if you want to solve for linear interpolation, use the linear interpolation formula which is:

    y = (x – x₁) * (y₂ – y₁) / (x₂ – x₁) + y₁

    where:
    (x₁, y₁) refer to the coordinates of the 1st known data point
    (x₂, y₂) refer to the coordinates of 2nd first known data point
    (x, y) refer to the coordinates of the point you’re solving for

    This formula is exactly the same as the extrapolation formula. Keep in mind that extrapolation often provides you with a result that’s not confirmed by any experimental data. This is why it’s more recommended to use interpolation.

    What is quadratic interpolation?

    We can best define quadratic interpolation using a formula. If you had a table of values

    yi=f(xi),0≤i≤2n

    On each of the intervals [x2j,x2j+2],0≤j≤n−1, you would use the quadratic interpolating polynomial on the interval for the interpolation of the data.

    How do you do linear interpolation in Excel?

    Interpolation refers to a method you can use to determine a future or present value factor when the exact value doesn’t appear on the value table. Interpolation assumes that any change between two given values is linear with an insignificant margin of error.

    Apart from using an interpolation calculator, you can also perform linear interpolation in Excel. For this, you need to input a specific formula which performs the linear interpolation method by solving for the step value of interpolation. The Excel formula to use is:

    =(end-start)/(ROW(end)-ROW(start))

    where:
    end refers to the address of the larger number’s cell
    start refers to the address of the smaller number’s cell