The equation and what each term is
For a flat wall cooled from both faces, the cooling time is the wall squared, divided by pi squared times the thermal diffusivity, times the natural log of four over pi times the temperature ratio. The temperature ratio is the melt minus the mould surface, over the ejection temperature minus the mould surface. Nothing in it is adjustable except by changing the part, the resin or the process.
Put the form defaults through it. A 2.5 mm wall, melt at 230 C, mould surface at 40 C, ejection at 90 C, diffusivity 0.09 mm2/s. The ratio is 190 over 50, which is 3.8. Four over pi times 3.8 is 4.838, and its log is 1.577. The wall squared is 6.25 and pi squared times 0.09 is 0.888, so the time is 6.25 divided by 0.888, times 1.577 — 11.1 seconds. Add the 8 seconds the form allows for everything else and the cycle is 19.1 seconds.
Why the wall is the whole argument
The wall appears squared and nothing else does. Drop the same part from 2.5 mm to 1.25 mm and the cooling falls from 11.1 seconds to 2.8, and the cycle from 19.1 to 10.8 — the machine makes 333 cycles an hour instead of 189. Go the other way to 3.75 mm and cooling is 25 seconds, cycle 33, and 109 cycles an hour.
Every other lever is weaker than that. Dropping the mould surface from 40 C to 20 C on the original wall takes the cooling from 11.1 seconds to 9.4, worth about 9 percent of the cycle, and it costs chiller capacity and brings condensation and a different set of part properties with it. Coring out a thick section costs a CAD afternoon and is worth four times as much.
Ejection temperature is the soft number
It is the input people guess at and the one the answer moves on most after the wall. Take the same part and change the ejection temperature from 90 C to 100 C: the ratio drops from 3.8 to 3.17 and cooling falls to 9.8 seconds. Drop it to 80 C instead and cooling rises to 12.7. That is a 26 percent swing across a range people pick by feel.
The honest way to pin it down is on the press. Shorten the cooling until the part comes out marked or distorted, back off, and work the temperature backwards from the time you settled on. After that the page is calibrated to your part rather than to a number off a datasheet.
What the model leaves out
Heat of crystallisation, which on a semi crystalline resin is real energy that has to leave the part and which this equation has no term for, so the true time runs above the calculated one. Variation in the mould surface temperature, which is treated here as one number everywhere and for the whole cycle. The heat still arriving during pack. And the cooling layout, which decides whether the thick section has any water near it at all.
None of that makes the equation useless. It makes it a comparison tool: the ratio between two walls, two resins or two ejection temperatures survives all four omissions, even where the absolute seconds do not.
Questions people ask
What is the cooling time formula for injection molding?
For a flat wall it is the wall thickness squared, divided by pi squared times the thermal diffusivity, multiplied by the natural log of four over pi times the ratio of melt minus mold temperature to ejection minus mold temperature. For a round section the wall squared becomes the radius squared, pi squared becomes 5.783, and four over pi becomes 1.602. Both are the first term of the series solution to one dimensional conduction, which is why they are only ever an estimate.
Why does halving the wall thickness cut cooling to a quarter?
Because thickness enters the equation squared and nothing else does. Heat has to travel to the surface, the distance is half, and the time to cover it goes as the distance squared. On the default part that takes 11.1 seconds down to 2.8. It is the largest single lever anybody has on a moulding cycle and it is pulled in CAD, not on the press.
Where do I get a thermal diffusivity value?
From the resin datasheet, either directly or as conductivity divided by density times specific heat, all read at the temperatures you run. The supplier will give it if the datasheet does not. It is a field on this form rather than a built in number because it varies with the grade, the filler, the crystallinity and the temperature, and no calculator can know which resin is in the hopper.
Should I use the centre or the average temperature basis?
The centre basis asks when the middle of the section has reached the ejection temperature and is the more conservative of the two. The average basis asks when the section as a whole has, and comes out shorter — on the default part 7.9 seconds against 11.1. Which matches reality depends on whether the part ejects on skin stiffness or on being solid through, so pick whichever agrees with the press and stay with it rather than switching to get a number you like.
Does this include the time to fill and pack?
No. It is the cooling term only, from the moment the section is at melt temperature. Injection, pack, mould open, ejection and any robot time go in the field for the rest of the cycle, which is added to the cooling to give the total. On many parts pack overlaps the start of cooling, in which case the calculated cooling already covers part of it and the field should hold only what genuinely happens outside it.