Calculus How To

Extrapolation & Interpolation: What Are They?

Share on

What is Extrapolation?

Extrapolation is a way to make guesses about the future or about some hypothetical situation based on data that you already know. You’re basically taking your “best guess”. For example, let’s say your pay increases average $200 per year. You can extrapolate and say that in 10 years, your pay should be about $2,000 higher than today.

The black line shows the data points. The dashed line shows a hypothetical extrapolation.

The black line shows the data points. The dashed line shows a hypothetical extrapolation.

What is Interpolation?

Interpolation allows you to estimate within a data set; it’s a tool to go beyond the data. It comes with a high degree of uncertainty. For example, let’s say you measure how many customers you get every day for a week: 200, 370, 120, 310, 150, 70, 90. According to that number, you should get just under 10 customers per hour (1,310 customers/ 168 hours in a week). Let’s say you staff your business 24-7 to deal with those hourly customers. You’re probably going to get zero customers at night and on the weekends, therefore wasting resources. (Note: a better way to figure out peak times is the Poisson Distribution).

Real Life Uses

You extrapolate to some degree in your daily life. For example, you might look forward to your monthly paycheck and you assume that you’re going to get it based on known data (the fact that you’ve got paid monthly, on-time for the last year). But what if your company goes bankrupt? Or the market crashes? Or the bank mistakenly freezes your bank account? In this particular case, extrapolation has a fair amount of certainty (you’re probably going to get your paycheck), but that isn’t always the case.

Use in Statistics

Extrapolation can mean several things in statistics, but they all involve assumption and conjecture (extrapolation is far from an exact science!):

  1. The extension of a statistical method where you assume similar methods will be used.
  2. The projection, extension, or expansion of your known experience into an area that you do not know or that you haven’t experienced yet.
  3. The use of equations to fit data to a curve. You then use the equation to make conjectures. This is known as curve fitting or regression, which can get quite complex, with the use of tools like the Correlation Coefficient.

Other Practical Uses

Extrapolation is used in many scientific fields, like in chemistry and engineering where extrapolation is often necessary. For example, if you know the current voltages of a particular system, you can extrapolate that data to predict how the system might respond to higher voltages.

Cautions with Use

In general, you should extrapolate with caution. For example, you might be able to rely on a steady paycheck coming in for a few months or years, but it probably wouldn’t be a good idea to assume that same company is going to be still paying you 20 years down the road!


Everitt, B. S.; Skrondal, A. (2010), The Cambridge Dictionary of Statistics, Cambridge University Press.

Stephanie Glen. "Extrapolation & Interpolation: What Are They?" From Calculus for the rest of us!

Need help with a homework or test question? With Chegg Study, you can get step-by-step solutions to your questions from an expert in the field. Your first 30 minutes with a Chegg tutor is free!