Dtyjlui

If you want to be able to pick up on a song by ear, sight reading won't be a lot of help. (Downvoters - please say why you did!).

Since your aim is to play by ear, and hit whatever notes and chords instinctively, then being able to read charts won't help at all.

As long as you are aware of what each chord comprises, and how they work with each other, and can play a bass line that flows, and use your ears for instant accuracy, carry on playing the way you do, as sight reading is a very different and diverse skill from playing by ear. Generally speaking, I find that players fall into one of the camps - great sight readers, or great 'play by earers'. There are very few players that I've worked with who are very good at both. I guess if one is better at one, then that gets favoured over the other, and strengthens more to the detriment of the other.

Looking at and considering the comments and answers - it would be worth a foray into sight reading. It might just be that, as you already have a way round the notes, that looking at how it's portrayed on the lines and spaces, it suddenly becomes pretty obvious how it all works. And you start thinking - actually, it's easier than I thought, I'll have a go. Certainly worth consideration. 'Cos then you have that extra bow to your fiddle, or whatever the phrase may be today...

EDIT: something that will help you playing by ear is to know several scales, in many keys. Reason for this is that when you've found/decided on a key for a piece, and are aware of whether it's using say, blues scale, pent. scale, minor scale notes, it usually automatically means certain notes won't be played. So you will save time and effort not even trying those notes. Simple example, in key C, chances are you won't be needing D♭.

You can only play 'by ear' using musical elements that you're familiar with. So you need to get familiar with LOTS of music, in LOTS of styles - what it sounds like, and what your fingers have to do to get that sound.

Sorry, @Tim, but by far the most efficient way to do this is by reading lots of music. Not necessarily by perfecting a small number of difficult pieces (though you need technique too.)

Develop your 'by ear' playing skills AND your sightreading skills. They will nurture each other. Remember, the aim is to play the piece. If the printed music is available, it's foolish to reject that route!

Before I start, I will mention that I can really only play (guitar, sing and drums) by ear. If I learn from something written down, I'm much slower and can't read music so it has to be tab or chord notation. In honesty, I've never needed to go further than this in order to get a LOT of enjoyment from music.

Learning a piece by ear is ace fun, and you'll get probably 90% of popular tunes easily. However when you get to something that's hard to hear (!) in detail, you probably need to see it written down.

The difference is that 'by ear' gives you a feel for it, and a good hint at a piece. Seeing it written down tells you THE CORRRECT THING TO PLAY.

However this doesn't necessarily mean sight-reading. It could be just reading the notes of a tricky part and getting them sorted at your own pace, then getting the rest right by ear.

Perhaps it depends on the kind of music you're playing. If you're playing popular tunes, or something jazzy etc then by-ear is usually enough detail to get them learnt. If you're playing tricky classical pieces with intricate arpeggias etc, then maybe getting the right detail becomes more important.

Incidentally, I'm in awe of people who can sight-read. It's not something I aspire to myself because I enjoy the freedom of playing things how I hear them rather than being too dictated-to. But watching someone sight read a piece is to me quite astonishing.
I've had the same thing said by sight-readers about those who can play by ear, which underlines Tim's answer.

There is a common misconception on what "playing by ear" is. Many people think it is knowing what a melody is then hunting and pecking on your instrument for the correct notes. One wouldn't walk through a mine field like that so why would we attempt to perform like that? Because you probably know how to read and sound out words, I can say "cat" and you will be able to guess KAT or CAT or maybe even QHUAT. That is because you have mastered the alphabet and sounding out with your mind's ear.

True playing by ear is more cerebral than you think. It involves knowing all your scales, some degree of music theory and the ability to see the notes in your mind's eye when you hear them. Here is what I mean.

I can hear the tune ODE TO JOY in my head. Because I sing a lot but sing by visualizing sheet music (usually by the pool) in my head, I just know that the melody starts on the third. I can hear it start on the third. From there, as I hear each pitch, I just know what the numeric values are:
33455432 1123322 33455432 1123211
As I hum, I simply know those corresponding numbers because I only think in numbers. An added benefit to reading by numbers and not letters is that I can then transpose that into any key. Just start on the third of any scale and play those numbers. Poof, you're a genius. If I am improvising and I wish to quote this melody, I only have to aim for the third. There is no hunt and peck, there is no guessing, there is no "playing by ear." It is all brain conversion from inner ear.

The good news is that you can practice this anywhere without the need for a piano. Lying in bed, driving a car, lounging by the pool, hiking through the woods, listening to the homily . . . Also, whenever you hear music, don't just hum along, listen or ignore it, use it to practice. What is the starting pitch? Is it on the 1, 3, 5? Does the bridge change keys a fourth higher? What is the chord progression? You can hear all these things and translate them to numbers on the fly. WITH PRACTICE.

Some teachers teach the solfege method but I find numbers easier and if I am jamming with other musicians I can just hold up a finger. I can't hold up a SOL.

Try it with something simple such as MARY HAD A LITTLE LAMB. It starts on the third. Don't use just your ear, employ the brain. Don't guess, know. I'll wait. My brain tells me the pitches are 3212333 222 355 3212333322321. Did you get those too? Go test them on the piano in any key.

Now, someone is going to chime in saying "That is fine and dandy for melody but you can't do that with larger works, fugues or etudes." What they are really saying is THEY can't do it. Because I only read by numbers I can see all the numbers. If they read by letters, they see letters. I can't fly an airplane so therefore nobody can. All you need to do is know your scales and intervals and what each interval sounds like - away from the piano.

As an added bonus, you will find memorization to come rather quickly. Actually you are not "memorizing" notes. Your ear will hear and you'll just know or read in your mind. I don't have GOLDILOCKS AND THE THREE BEARS memorized but I can fake the story.

This will be offensive to many people but I consider letter readers to be musically illiterate. Like, they can speak but not read. My folk group musicians are all excellent readers. They can play anything I put before them. However, if I ask them to raise it a third, they can't. Why? They really don't know what they are doing. Matching dots to a key is so easy a parrot can do it. In the following video, I doubt the bird knows what a square, circle or isosceles trapezium is. This bird is not genius, it is just matching shapes like it was trained to do. BTW, this is how Beethoven could compose while deaf. His ear may have been deaf but his brain wasn't. Go ahead, "hum" something in your brain. What were the numbers?
Parrot matches shapes

A good way to practice is to go steal a hymnbook from your local Protestant church (God will forgive you) and away from the piano, number sing all four parts. Start with just one line at a time (SAT or B). Soon you will see all four parts by their numbers. Hymns are great to start with because they rarely go beyond and octave, the notes are repetitive, the form is often AABA and all the notes are chord tones. Study, study, study, study, study. Then sit at the piano. Oh, if you don't want to beg, borrow or steal, you can check out hymnary.org but taking a book with you means you can "practice" anywhere, anytime.

My end goal is to eventually be able to play any song by ear and put
my own variation on it.

Same here that was my goal too, esp if you're into improvising and composing you need to play by ear mainly. Even the Beatles didn't know how to read music.

I played piano as a kid for years reading sheet music, played guitar for a few more years without knowing much theory, just jamming around to random tabs and improvising random patterns. It took me about 10 years to realize I had learned music all wrong.

I had an epiphany when I realized that music should be played just like we whistle, using muscle memory. Another epiphany came to me when I realized that all major scales are simply shifted in pitch but are essentially the same pattern "do re mi fa so etc", that and that 80% or so songs are in major. Then another epiphany when I realized I've always had a propensity for the minor scale, and more epiphanies along the way.

I then went back to a piano and took it upon myself to play by ear hundreds of songs that I always had in my mind throughout life and ask any question I had on this site. It took me about two years of about 3-4 hours a day but I was committed. Just knowing as many songs as you can, that you personally like and what makes them tick. So like what scales and chords they're using. But not focusing on chords names, more so focusing on their function and relative notation (I, ii, IV, V7, etc) so that you can play them in other keys.

My biggest suggestion is to take very easy songs and play them in all keys. It's like playing scales but practicing scales limits you to playing minor second and major second intervals. That's not enough. So take a tune, for example "Amazing Grace" and play it in all keys. That way you start developing your muscle memory to what different intervals sound like, and you start training yourself to know where
the notes and chords are in all keys.

At first it can take days to figure out a song but with enough practice it then takes minutes, or even seconds.

Also the only thing you need is a piece of paper and write what songs you know on it. And constantly work and refine them and add more songs to that list. There are still old songs I know that I'm constantly fitting new harmonies in and polishing what they sound like, adding embellishments, etc.

But you need theory if you go by ear: so know how to create a scale, know how to get chords from a scale, play major/minor, etc. Once you have theory + ear then you have music. You'll hear ANY song on the radio and you'll know how to recreate it instantly when you have a keyboard next to you, and you'll be able to improvise your own music, it's very liberating. You'll begin to appreciate how every song around you follows the same basic rules.