[Mini Guide] Keep track of your units!

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Introduction

This is going to be a more general guide about math and related subjects rather than strictly tech, but I think it is useful information for virtually anyone.  I'll be keeping it very simple here, not going into functions and exponents however.

 

Have you ever tried working something out and:

• forgot what a value was or represented,
• not known whether you should be dividing or multiplying,
• not known what you should do next in a calculation, or
• been unsure if your answer is reasonable?

Hopefully what I'm going to describe will help in all of these areas!

 

Process

1. Imagine a "linkage" between the units involved.  You need to find a way to bridge the gap between the information you know and the information you want to determine.  Start finding any values that will let you do that.  You'll know you're on the right path when it includes one or more units from one or more pieces of the information you either know or want to know.
2. Break it down.  If you don't know a certain unit, or can't work with it in the current form, look up the equivalent forms.  Odds are they will give you a more intuitive understanding of what physical quantity or property is being represented, and will allow you to work with it more easily.
3. Combine.  Multiply the conversion factors and other equation elements together, making sure that units you don't want in your final answer cancel out along the way, and ones you want are preserved or come into play.

If your calculation gives a result that doesn't have the units you were expecting, it was either done wrong, or at the very least isn't telling you what you originally wanted to know.

 

Example

• We want to know the annual cost of powering some electrical equipment that has a constant power draw when active
• We know the power draw in W (Watts), and want to know $/year

Time to fill in the blanks

• 250 W consumption
• 5 hours per day, 300 days per year
• 12 cents per kWh
• 0.001 kWh per Wh
• 0.01 $ per cent

We can now combine all this information:

1. Multiply the known values:
2. Eliminate terms:
3. Observe the answer:

Try it yourself!  One thing you will likely get caught out by is should you use 0.001 kWh/Wh, or 1000 Wh/kWh?  If you want the simplicity of multiplying everything and not having to divide, choose the one that lets the units work out.  If you use the wrong one it won't work.  Observe:

1. 
2. 

Now, of course this can be simplified further since kW and W are just different magnitudes of the same unit, but you have to make sure you keep track of this!  Don't let anything cancel something that isn't identical.  In this case, if we get rid of the watts, we have a stray "kilo squared" term, which is nonsensical, but also hints at the incorrect magnitude of our answer.  You could interpret it as 45 million micro dollars per year, which is the right value, but no one would ever write such a thing.

 

Conclusion

It can be tempting to just throw all of the numbers you plan to work with into your calculator, or your head, and imagine that you did it all right, and if you're good with this sort of thing, you probably did, but it never hurts to double check, and if you're someone who struggles to keep track of things, this should really help you follow the process without getting lost, and verify that what you've got at the end makes sense.

[Stormseeker9]

Fuck I suck at math can’t figure it out... mine is 24/7 at €0.25c/kWh system consumption around 250w too (only GPU folding) but that consumption is per what? Second,hour, day? That’s where I’m most confused 

[DrMacintosh]

I passed Intro to Chem with a 70% in College. I've done enough stoichiometry to last 4 lifetimes. 

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41 minutes ago, Stormseeker9 said:

Fuck I suck at math can’t figure it out... mine is 24/7 at €0.25c/kWh system consumption around 250w too (only GPU folding) but that consumption is per what? Second,hour, day? That’s where I’m most confused 

Energy is a quantity, like mass, or distance, and power is the rate as which you use energy.  Watts is power, aka, energy per second, specifically Joules per second.  kWh is also a unit of energy, like Joules, because it's power x time, which just makes it back into energy.  This is what I mean by point 2 under "process".  If you don't know what watts is for example, it's going to be a struggle so, my recommendation whenever this happens is to look it up and figure out how it breaks down.  Hopefully when you see it in pieces the concept of what is being represented will make sense.

[Stormseeker9]

4 minutes ago, Ryan_Vickers said:

Energy is a quantity, like mass, or distance, and power is the rate as which you use energy.  Watts is power, aka, energy per second, specifically Joules per second.  kWh is also a unit of energy, like Joules, because it's power x time, which just makes it back into energy.

1kwh = 1000W? in that case its like 1 euro an hour so EUR24 a day.. damn... that would mean EUR750 for 30 days? Surely im doing something wrong haha

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5 minutes ago, Stormseeker9 said:

1kwh = 1000W? in that case its like 1 euro an hour so EUR24 a day.. damn... that would mean EUR750 for 30 days? Surely im doing something wrong haha

Look closely, you've lost an hour in there 1 kWh = 1000 Wh, or 1 kW = 1000 W

[Stormseeker9]

4 minutes ago, Ryan_Vickers said:

Look closely, you've lost an hour in there 1 kWh = 1000 Wh, or 1 kW = 1000 W

So per 1000Wh = 0.025EUR = * 10 = 1 Kwh? which means 75EUR for the month? Sorry Math isn;t my strong part ..

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1 minute ago, Stormseeker9 said:

So per 1000Wh = 0.025EUR = * 10 = 1 Kwh? which means 75EUR for the month? Sorry Math isn;t my strong part ..

Don't worry about equals or equations, just start with the number you know and keep multiplying new values into it.

 

Start with your consumption in watts.  You said 250 so we'll use that.

250 W x 24 h/d x 365 d/y = 2190000 Wh/y

Now we'll change it to kWh

2190000 Wh/y x 0.001 kWh/Wh = 2190 kWh/y

Now factor in the price

2190 kWh/y x 0.25 €/kWh = 547.50 €/y

[Stormseeker9]

3 hours ago, Ryan_Vickers said:

Don't worry about equals or equations, just start with the number you know and keep multiplying new values into it.

 

Start with your consumption in watts.  You said 250 so we'll use that.

250 W x 24 h/d x 365 d/y = 2190000 Wh/y

Now we'll change it to kWh

2190000 Wh/y x 0.001 kWh/Wh = 2190 kWh/y

Now factor in the price

2190 kWh/y x 0.25 €/kWh = 547.50 €/y

Legend!! Thanks heaps.