What Are ao5 and ao12? How to Calculate Them, the Difference, and What mo3 and ao100 Mean
Rubik’s Cube results are often written as "ao5 11.95" or "ao12 13.02". An ao5 is an average of five solves, but you don't just add them up and divide by five: you first drop the single fastest and single slowest solve. If you don't know this rule, your own averages won't match your timer, and you won't know what to do when a DNF turns up. This guide explains how to calculate ao5 and ao12 with worked examples, how they differ from mo3, ao50 and ao100, how DNF and +2 are handled, how times are rounded to hundredths, and how all this relates to official WCA results.
ao5 is the average of 3 solves after dropping the fastest and slowest of 5
ao5 stands for average of 5. Take five consecutive times, remove the single fastest and the single slowest, and average the three that remain. It is usually read as "A-O-five" or "average of five", and people often just call it their "average".
Say your five times were these.
| Solve | Time | Treatment |
|---|---|---|
| 1st | 12.34 | Counted |
| 2nd | 11.02 | Counted |
| 3rd | 13.50 | Dropped as the slowest |
| 4th | 12.50 | Counted |
| 5th | 10.98 | Dropped as the fastest |
Without the fastest and slowest, 12.34 + 11.02 + 12.50 = 35.86 seconds. Divide by 3 to get 11.953…, round to hundredths, and the ao5 is 11.95. A plain average of all five would be 12.07, so the ao5 leaves out both the lucky 10.98 and the 13.50 where something went wrong.
Why drop the fastest and slowest?
Speedcubing times swing a lot with lucky or unlucky scrambles and momentary mistakes. A solve where the cross happened to take one move, or where the PLL skipped, is faster than your real level; a solve where you skipped a step and had to recover is much slower. Throwing away one solve at each end shrinks the effect of luck, so the ao5 is closer to how fast you usually solve.
- Best single: your fastest one-off solve. Luck plays a big part, so a new PB single is exciting but not a great measure of skill
- ao5: with both ends dropped, one disaster or one lucky solve doesn't move it much
- ao12 and ao100: more solves, so an even steadier picture of your current level
At official WCA (World Cube Association) competitions, 3×3 and many other events are ranked by the ao5 of five solves. So the ao5 is both a practice benchmark and your actual competition result.
ao12, ao50 and ao100 drop 5% (rounded up) at each end
ao12 is the average of 12 consecutive solves. As with ao5, you drop the single fastest and slowest and average the remaining 10. For ao50 and ao100, most timers (including csTimer) drop 5% of the solves at each end, rounded up.
| Type | Solves | Dropped (each end) | Solves averaged | Becomes DNF when |
|---|---|---|---|---|
| mo3 | 3 | 0 | 3 | Any DNF |
| ao5 | 5 | 1 (5 × 5% = 0.25 → rounded up) | 3 | 2 or more DNFs |
| ao12 | 12 | 1 (12 × 5% = 0.6 → rounded up) | 10 | 2 or more DNFs |
| ao50 | 50 | 3 (50 × 5% = 2.5 → rounded up) | 44 | 4 or more DNFs |
| ao100 | 100 | 5 (100 × 5% = 5) | 90 | 6 or more DNFs |
Here is an ao12 example. Suppose your 12 times were 14.21, 13.05, 15.80, 12.66, 13.92, 14.48, DNF, 13.37, 12.98, 14.03, 13.71 and 11.89. A DNF counts as the slowest result, so it is dropped as the slowest, and the fastest, 11.89, is dropped too. The remaining 10 add up to 13.05 + 15.80 + 12.66 + 13.92 + 14.48 + 13.37 + 12.98 + 14.03 + 13.71 + 14.21 = 138.21 seconds. Divided by 10 that is 13.821, which rounds to an ao12 of 13.82.
ao50 and ao100 are good for seeing how consistent you are over a long session. A PB ao5 only needs five good solves in a row, but an ao100 averages a hundred, so your practice shows up directly in the number. Raising your goal from "sub-20 ao5" to "sub-20 ao100" tells you whether you can really get under 20 seconds consistently.
mo3 is a plain mean of 3 with nothing dropped
mo3 stands for mean of 3: the average of three times with nothing removed. To distinguish it from an average (with ends trimmed), a plain average is called a mean. For 12.40, 13.10 and 11.95, the total is 37.45; divided by 3 that is 12.483…, so the mo3 is 12.48.
- 6×6 and 7×7: each solve is long and five would take too much time, so competitions rank these by mo3
- 3×3 Fewest Moves (FMC): most competitions use the mean of three attempts' move counts
- Blindfolded (3BLD etc.): ranked by the best of 3. The mo3 is recorded for reference
Because mo3 drops nothing, a single DNF makes the mo3 a DNF. In an ao5 one mistake can be dropped, but in a mo3 one mistake is fatal. When practising 6×6 and 7×7, prioritising finishing every solve cleanly over raw speed will improve your mo3.
Calculating with DNF and +2
A DNF (Did Not Finish) means no result. When averaging, it is treated as infinitely slow. A +2 means two seconds are added to the time, and that time is used as is. Both are penalties given for things like going over the inspection time or stopping the timer when the cube isn't solved; the details are in the 15-second inspection rule, +2 and DNF.
| Five times | ao5 | Why |
|---|---|---|
| 12.10, 13.25, 11.80, 12.95, DNF | 12.77 | The DNF is dropped as the slowest and 11.80 as the fastest |
| 12.10, 13.25+, 11.80, 12.95, 12.60 | 12.55 | 13.25+ counts as 15.25 and is dropped as the slowest |
| 12.10, DNF, 11.80, DNF, 12.60 | DNF | Two DNFs but only one can be dropped, so the average is a DNF |
In the first example the counting times are 12.10, 13.25 and 12.95: (12.10 + 13.25 + 12.95) ÷ 3 = 12.766… → 12.77. In the second, 12.10, 12.95 and 12.60 average 12.55. If the +2 solve ends up as the slowest and is dropped, it doesn't affect the ao5 at all. As in the third example, when there are more DNFs than can be dropped, the average itself is a DNF.
Rounding to hundredths: singles are truncated, averages are rounded
Under the WCA Regulations, single results under 10 minutes are truncated to hundredths of a second, and averages are rounded to the nearest hundredth. A solve of 12.348 seconds is recorded as 12.34; an average of 11.9533… becomes 11.95 and 11.955 becomes 11.96.
Some timers display thousandths, so the same solves can give averages that differ by 0.01. If you want to compare with competition results, truncate singles to hundredths before averaging so your numbers match.
How to calculate ao5 and ao12 automatically
Working it out by hand every time is tedious, so let the timer do it. The Rubik’s Cube Timer updates the current and best mo3, ao5, ao12, ao50 and ao100 after every solve, and puts brackets round dropped times in the list.
- 1
Choose a puzzle and time your solves
Choose 3×3, 2×2, 4×4 or 3×3 One-Handed and time with the space bar or a tap. Records are kept separately for each puzzle.
- 2
Check current and best values in the table
ao5 appears after 5 solves and ao12 after 12. "Current" is the latest value and "Best" is the best value from any earlier stretch.
- 3
Paste times from another timer to calculate
Paste something like 12.34, 11.02, DNF, 13.50+ into the "ao5/ao12 calculator" tab to see the average and which times are dropped. Handy for checking competition results, too.
- 4
See where the next solve can take you
After four solves, the timer shows how good or bad your ao5 can end up depending on the fifth. See BPA and WPA: the time you need for a target ao5 for details.
If you can't decide whether to aim at ao5 or ao12, watch your ao12 for daily practice and your ao5 if you are preparing for a competition. How to structure your practice is covered in How to use a cube timer and practice to improve your times.
FAQ
- What's a simple way to calculate an ao5?
- From your five times, drop the single fastest and the single slowest, add the remaining three and divide by 3. For 12.34, 11.02, 13.50, 12.50 and 10.98, drop 10.98 and 13.50 and average the other three: 11.95.
- What's the difference between ao5 and ao12?
- The number of solves and how many are counted. ao5 averages 3 solves after dropping one at each end of 5; ao12 averages 10 after dropping one at each end of 12. ao12 uses more solves and is less affected by luck, so it is closer to your true level.
- How many solves are dropped in an ao100?
- Most timers drop 5% (rounded up) at each end, so an ao100 averages 90 solves after dropping the 5 fastest and 5 slowest. An ao50 drops 3 at each end and averages 44.
- Are mo3 and ao3 the same?
- Three-solve averages are normally given as mo3 (mean of 3), with nothing dropped. Dropping both ends of three would leave only one solve, so "ao3" is rarely used. 6×6 and 7×7 competitions are ranked by mo3.
- What happens to my ao5 if one solve is a DNF?
- A DNF counts as the slowest result and is dropped as the slowest. With just one DNF, your ao5 is the average of the remaining four minus the fastest. Two or more DNFs make the ao5 a DNF.
- Does the WCA round or truncate averages?
- Under the WCA Regulations, singles are truncated to hundredths and averages are rounded to the nearest hundredth. An average of 11.955 seconds is recorded as 11.96.
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