Explained: Linear Interpolation [Math]

In this video, I explain how to obtain the equation for linear interpolation between two points. I then go through a simple example.
Linear interpolation can be useful when you need data at points where data does not exist. This happens a lot when looking at tabulated data. Here are some examples of tabulated data where linear interpolation can come in handy:
- Steam/vapor tables in thermodynamics
- Property tables in heat transfer
- Normal shock tables and isentropic relations tables in gas dynamics
In the video linked to below, I show you how to program this equation into a graphing calculator (TI-83), so you can use it on exams or whenever you need a quick estimate.
goo.gl/ntTuKl

[@ercm2393]

Great video!!! I am here because I am learning how to control animations through scripts in Virtual Reality and Linear Interpolations is one of the most important factors that makes it happen! Just wanted to learn it a little deeper! Thanks for sharing!

[@JoshTheEngineer]

My pleasure! Linear interpolation shows up everywhere!

[@KevRyanCG]

7 months on but the very same, though for me it's FX stuff in Houdini

[@slimmyblanco9004]

Gotta join you guys here, though I’m learning it for substance designer. I know this can be a helpful tool that can be applied to many other 3D packages.

[@clauderobotham6261]

Circumstances required me to revisit interpolation for the first time in decades (since high school). Your explanation was very cogent and I think I actually understand it better now than I did then. Thanks, Josh.

[@JoshTheEngineer]

Awesome, thanks for watching!

[@ezenweregozie5016]

Thanks so much for this......I have been wasting my time searching for the derivation. I wish all teachers should be like you. So direct and straightforward.

[@JoshTheEngineer]

Thanks, I appreciate it!

[@makrooneey7604]

Great explanation... Having an exam later today... & this helped

[@321Roost]

Thanks so much for showing the graphical method of linear interpolation. I am used to doing it algebraically. Very good instructive video!

[@PhoenixA380]

Nice, simple, clean and straight to the point, thank you very much!

[@Infiniband11]

Thank you for this great, simple, and easy-to-understand explanation.

[@natashadavis5035]

This was so simple the way you explained it, thank you for your organized explanation!

[@JoshTheEngineer]

You're welcome!

[@makrooneey7604]

Hi natasha

[@Mulkek]

Thanks, and it's so easy & simple!

[@meraklmuskulpesent8313]

Thank you so much! Your way of teaching things is plain and effective.

[@matone4374]

love the fact that he uses as an example the exact thing i want to use it on XD . (thermodynamics)

[@drfoxy3190]

I wish that I have a teacher like you for chemistry ! :D

[@JoshTheEngineer]

Ha, thank you!

[@kevinmitsui3002]

Thank you Josh

[@stashatstake]

Thank you I needed to understand this to use a built-in function in a game engine that I am using.

[@JoshTheEngineer]

You're welcome!

[@ginarapp6625]

Thanks so much for the video ! Really helpful for my CFA study

[@JoshTheEngineer]

Glad I could help!

[@isaissb]

Around 3:19 you say something like "we'll be able to get to the new.. Y location". This conclusion sounds a little lackluster, but overall good explanation. Multiplying the slope by the change in x will give you the change in y, which is then added to y1 to get to the new Y location.

[@JoshTheEngineer]

Thanks for the feedback! Maybe it sounds a little anticlimactic, but that's because this topic isn't that exciting to begin with.

[@seanmcclanahan6975]

My brother directed me to this cuz I was confused. Now I'm not 😀 you taught this beautifully and I'll check your channel if I am confused in the future :) Subscribed

[@JoshTheEngineer]

Awesome, glad I could help out!

[@MrSazid1]

Dude you are good. I really appreciate how u explained to get y value just multiply the slope with x distance add it to y. I have hard time to interpret equations in plain english. thank you very much.

[@JoshTheEngineer]

Thanks! Yea, the equation can look complicated, but it's actually pretty simple when you look at what each term means.

[@KitLeskinen]

Thanks for good explanation! Now I understand.

[@JoshTheEngineer]

Awesome!

[@lahiru3908]

Amazing explanation

[@JoshTheEngineer]

Thank you!

[@s.r.coachingclasses.1770]

Respect you sir, I was finding this type of questions, thank you very much sir.

[@JoshTheEngineer]

You're welcome!

[@sunliangliew9273]

Simple and easy to understand

[@rosette_renah]

Beautiful video

[@JoshTheEngineer]

Thanks!

[@maggysantana3878]

Joe. Thanks to show how is the formular is applicable to the problem, but you forgot to show step by step how to calculate those values so it can give you those results you plug in. That is the matris of the problem where the knowledge is getting strengths, soo please keep in mind that... let see if you have someone who doesn't never done interpolation before... he/she will be lost... so keep that in mind in your next video. Thanks

[@JoshTheEngineer]

Thanks for the suggestion Maggy!

[@DrTomb]

GREAT VIDEA!!! thank you so much

[@arnavgupta970]

well explained thanks for making this easy

[@clementchidozie4009]

You did a great job! Thanks a lot.

[@JoshTheEngineer]

Thanks!

[@dilshadxahmad]

Great Video...!!! You are the motivation for me, to be a good Industrial Engineer :)

[@JoshTheEngineer]

Awesome, keep it up!

[@richardgarrison8328]

Much appreciated

[@jbz2513]

Great video.. You explained it in a way that is hard not to forget. I have a question. Why did you take y - y1 and x - x1 and not y2 - y and x2 - x? And based on this you should get the same values yes? Because linear interpolation assumes the same slope?

[@punaydang2948]

maybe because it is that from pt(x1,y1) to (x2,y2) the slope of line is constant and when ever we take slope we take it in upward direction i.e why it is rise

[@marceloamado6223]

gigachad thank you 👍👍

[@hadan90]

Very clear explanation. Thank you.

[@JoshTheEngineer]

You're welcome!

[@A31Chris]

I thought that was good. Thank you. I tried a couple other vids and they were crap.

[@khalidalmamari95]

Thank you soooooo much 🌹👌

[@JoshTheEngineer]

No problem!

[@HeyEveryoneHi]

Thank you !

[@JoshTheEngineer]

You're welcome!

[@mxkep]

Well explained man! Have anything on polynomial interpolation?

[@JoshTheEngineer]

Thanks! And no, not yet, but it's on my to-do list, so stay tuned.

[@mxkep]

Okay great! I will for sure.

[@brimmed]

i guess i don't get why we make the assumption that the slope between y_2 and y_1 is equal to the slope between y and y_1. i'm studying for eit and it asked us to solve for area using trapezoidal rule for uneven segments. but we need interpolation because we do not have f(a = 12), we have f(0) and f(15). what if f(12) = 1 million f(0) = 0, and f(15) = 25

[@dwaynemckinnon9922]

thanks, great job!!!!

[@JoshTheEngineer]

My pleasure!

[@hardikshrestha820]

Can you make video for quadratic interpolation? Thank you by the way😀

[@nazarnazark516]

Super video... Very useful

[@JoshTheEngineer]

Thanks!

[@siddhayan123]

how can i get a value Which is out of the table (eg. 310 for your example).... please reply.

[@JoshTheEngineer]

If you mean that the value you want is outside the bounds of the table minimum and maximum values, then you'll have to extrapolate. It works the same as interpolation, but you have to be more careful with extrapolation.

[@muhammadrizvi8436]

Thanks for sharing this video. I have a question, I'm working data compression and reconstruction techniques through interpolation. Actually I had 20,000 data points and I successfully compressed it into 244 data points. Now I want to reconstruct the data again but I'm stuck how to implement the linear interpolation to reconstruct the data again. Can you assist me? I will be waiting for your kind reply. Regards

[@williamhjorth4284]

damn you have waited a long time

[@ediwawerz]

Thank you!!!!

[@JoshTheEngineer]

You're welcome!

[@ediwawerz]

[@kausalyabaissonale4804]

It is a good video!!!

[@JoshTheEngineer]

Thank you!

[@TheVoiceOfChaos]

i was lost at green line

[@CTWpod]

Go Bills!

[@JoshTheEngineer]

A man of culture, I see.