What Is TPS on a Rubik's Cube? How Fast Is Fast?

What is TPS?

According to the Speedsolving Wiki, TPS is the average number of moves per second, measured over one algorithm or a whole solve.

Working it out is easy:

TPS = number of moves ÷ number of seconds

For example: you finish a solve in 90 seconds and count 120 moves. Your TPS is 120 ÷ 90, about 1.3 moves per second.

Flip the formula around and you get the most important idea in this post:

Solve time = number of moves ÷ TPS

So there are two ways to solve faster: turn faster (raise your TPS), or use fewer moves. As you will see below, the second way is usually easier.

How do you count moves?

One move is one turn of one face. The example below is 4 moves: R, U, R' and U'.

1. You start with (input)
3. After the formula

There are a few different ways of counting, called "metrics". The Speedsolving Wiki describes four common ones:

For TPS, cubers usually use HTM or STM. If you are a beginner and only turn the outer faces, both give the same answer: every letter in an algorithm is one move, R2 included.

If the letters R, U and F are still new to you, have a look at Rubik's Cube notation for beginners first.

How to measure your own TPS

You don't need any special kit. There are two ways:

1. Measure it on one algorithm. Pick an algorithm you know by heart, time yourself doing it, then divide the number of moves by the number of seconds. For example, the T-perm below has 14 moves:

R U R' U' R' F R2 U' R' U' R U R' F'

If you do it all in 2 seconds, your TPS on this algorithm is 14 ÷ 2 = 7.

2. Measure it on a whole solve. Film your solve, count every move afterwards, then divide by the time on the timer. This takes more effort, but it gives you the real number.

These two numbers are always different. Your TPS on an algorithm you know well is always higher than your TPS for a whole solve, because during a solve you also have to stop and look for the next piece.

What counts as a fast TPS?

There is no official chart for TPS. But here are a few markers to give you an idea:

• Beginners: often stop a lot to think, so their TPS over a whole solve is usually much lower than on an algorithm they know well. The example at the start of this post (120 moves in 90 seconds) gives a TPS of about 1.3.
• Aiming for under 20 seconds: the Speedsolving Wiki gives the example of a method that averages 50 moves. To solve in under 20 seconds with it, you need a TPS of at least 2.5.
• The best in the world: in the post What Are The Limits? on CubeSkills, former world record holder Feliks Zemdegs gives the example of a 60-move solution at 10 TPS, which takes 6 seconds. He estimates the limit for an average with the CFOP method at around 11 to 12 TPS. This estimate is quite old now, so treat it as a rough marker, not a record.

In the same post, Feliks says that 100 of his solves, when reconstructed, averaged about 58 moves (STM). In other words, even the fastest cubers don't solve with very few moves. They solve with very few pauses.

Why do fewer moves matter more than turning fast?

Go back to the formula: time = number of moves ÷ TPS.

Take the example of 120 moves at a TPS of 1.3 (90 seconds):

• If you cut 30 moves and keep the same speed, you are down to 90 moves and solve in about 67 seconds.
• To get the same result without cutting a single move, you would have to turn about a third faster.

Cutting moves is usually easier, because it comes from understanding, not from your hands. Here are two examples.

Example 1: merge extra moves

Beginners often turn the top face three times in a row to bring a piece into place: U U U. Three clockwise turns give exactly the same result as one anticlockwise turn: U'. That saves you 2 moves.

In the same way, turning R twice in a row should be written and done as R2: one move instead of two.

Example 2: one white corner, two ways to put it in

In step 3 of the layer-by-layer method, you hold the cube with the yellow face on top and bring each white corner down to the bottom.

When the white corner is in the top layer, at the front right, with its white sticker facing up, the beginner way is to repeat R U R' U' three times, which is 12 moves:

For exactly that case, the algorithm below puts the corner in place in just 7 moves:

R U2 R' U' R U R'

Both ways finish the white layer, but the second one saves 5 moves. With four corners, you get four chances like this in every solve. You don't need this shortcut straight away: get comfortable solving with R U R' U' first, then add shortcuts like this one bit by bit.

Pausing less matters even more

In 2022, Kepler Boyce and Cornelis Storm went through 69 videos of Rubik's Cube solves at many skill levels frame by frame, along with a survey of 1,385 cubers (Journal of Emerging Investigators). They found that solve time is closely linked to the number of grip changes and whole-cube turns, the time spent pausing, the number of moves in the cross, the number of algorithms known, hand speed, and how long it takes to recognise the cases on the last layer.

Hand speed is just one item on that list. Most of the rest comes down to pausing less and making fewer wasted moves.

So when you watch a fast cuber solve, don't just look at their hands. Notice that they almost never stop.

How to raise your TPS without losing control

Once your solves are steady, you can practise hand speed. Three simple drills:

1. Six times R U R' U'. Repeat R U R' U' exactly 6 times (24 moves) and the cube goes back to how it started. Start from a solved cube, do it 6 times and time yourself. If the cube doesn't come back solved, you made a wrong turn somewhere. After 3 times, only 4 corners are out of place, as in the picture below:

1. You start with (input)
3. After the formula

Doing the 24 moves in 4 seconds means you are at 6 TPS on this algorithm.

2. Go slow but never stop. Solve the whole cube at a slow but steady speed, as if to a beat. The goal is to never come to a full stop. This is how you practise "look-ahead": while your hands are turning, your eyes are already looking for the next piece.

3. Practise algorithms with your fingers. Turn U with your index finger instead of your whole hand, and hold the cube so you need to change grip as little as possible. Fewer grip changes is also one of the factors the research by Boyce and Storm points to.

One general tip: turning faster than you can handle makes it easy to slip, lock up the cube, or get an algorithm wrong. A fast solve that goes wrong is much slower than a smooth, steady one. Use the EasyRubic 3x3 timer to keep track of your average, not just your best single.

Video

Want to see it in motion? The short video below from the BenTheCuber channel on YouTube shows more about the ideas in this post. The video belongs to that channel and is embedded straight from YouTube.

Sources

• Turns per second – Speedsolving.com Wiki
• Metric – Speedsolving.com Wiki
• What Are The Limits? – Feliks Zemdegs, CubeSkills
• Rubik's cube: What separates the fastest solvers from the rest? – Kepler Boyce, Cornelis Storm, Journal of Emerging Investigators (2022)