Can you mix 0w-40 and 30w oil together and get something like 15w oil? How would that math work? When is it a problem to mix to different types of oil together other than oil weight?
In order to calculate the resultant viscosity you'd likely need to take into account any number of things. The numbers in oil ratings relate to their kinematic viscosity when cold (the number preceding the "W" equates to 0 degrees Celsius) and hot (the number following the W is measured at 100 degrees Celsius). The higher the number, the more viscous (and therefore less "flowing") the oil is.
Modern oils are made by blending any number of component ingredients, not just mineral and / or synthetic oil. Oils may include viscosity improving polymers or viscosity modifiers which may affect non-identical grades differently. You also need to consider relative quantities when mixing oil. Finally, specific oil weight may be different weights so may not fully mix within the engine. If one grade is heavier than the other and therefore always sits at the bottom of the sump (which is where the oil pickup pipe scavenges from) you may find that the engine is then running only on this grade.
Personally, if I do not know what grade of engine oil had been used in my vehicle and I do not know when it was last changed (I have an inexpensively purchased Golf GTI in this state at the moment), I'll perform an oil change with new filter using the manufacturers recommended grade of oil for the vehicle.
If I have a vehicle which has had a recent oil change and is indicating low oil, I'll add a top up of the grade that the manufacturer recommends.
It's worth noting that manufacturers recommendations may alter geographically due to different ambient operating temperatures. Oils thicken up in cold environments so thinner oils would be used in arctic regions. Thicker oils would be used in desert regions as thinner oils do not protect against sheer forces quite so well when they become very hot.
The only real way to determine the viscosity rating of a mixture of oil (assuming it will mix and not settle out) would be to submit it to a chemistry lab for grading.
Oil is considered miscible, which means it will mix with other engine oils to form some sort of hybrid grade when mixing different viscosities. Here's a quote from an AMSOIL page when talking about what would be the resulting outcome of mixing 10W-30 and 15W-50:
Mixing two different motor oil weights to make your own custom viscosity does not work quite as simply as it sounds. There a couple of unknowns and even some potential complications that have to be considered.
As the additive formula used to construct each viscosity (10W-30 and 15W-50 in this case) can utilize different chemistry, there simply is no way to project how well the mixture will actually work and whether the longevity of the oil mix will be affected.
While the viscosity of the mixture may result in an engine oil somewhere in the SAE 40 range, where the “W” (winter viscosity) will end up is anyone’s guess. Again, different chemistry can be used to “build up” the viscosity of an engine oil, so mixing two from different viscosity ranges is not likely going to deliver the result that you desire.
And this just covers the viscosity of the oil. There are other factors to consider when you mix motor oils:
Another uncertainty is the shear stability of a mixture of two different weights. As the chemistries of the two oils can vary, there is no way to predict how well the blend will stand up to shearing forces and extreme heat. While it may not be a disaster, the safer choice would be using one type of motor oil that was formulated to perform at its best.
If you are in a pinch, you could certainly top-up your engine oil level with an oil from a different viscosity range. It may not be the end of the world, but we are not endorsing the practice of brewing your own custom motor oil formula for complete oil change intervals and especially not for racing purposes.
In other words, if you are in a pinch, it's better to run some kind of motor oil in your engine rather than running it dry. Other than that, stick to one grade of motor oil.
Another issue may arise when mixing motor oil, even of the same grade, but from two different manufacturers. Every manufacturer will have their own additive package, and therefore their own separate brew or concoction will occur. If you mix these motor oils together, you will not know the outcome of what chemicals you are throwing together. This combination of chemicals and additives could be severely detrimental to your engine's soft surfaces, such as bearings. It is oil's job to protect these surfaces, not destroy them, but this is exactly what you could possibly be doing.
Bottom line here is, don't mix engine oils, whether by grade or manufacture unless you have no other choice. Doing so may not give you your intended results.