# Voltage divider formula volt * kohm what equals?

I have query about when I have to solve the formula of the voltage divider. For example to solve the formula with respect to R1. My query is when I solve the formula at some point I have to multiply volt with kohm and the problem is from physics perception where can I multiply volt with kohm and with what equals (volts?) or the right way is to keep it kohm*volt like I write it and volt will gone at the last division?

• Tip: the SI standards specify 'V' or 'volt', etc. i.e., lowercase when spelt out. 'k' is for 'kilo' and 'K' for 'kelvin'. Then it's 'kΩ' or 'kilohm' but never 'kohm', 'kOhm', 'Kohm' or 'KOhm'. Apr 5, 2022 at 20:36
• @Transistor kohm is fine if you are limited to A-Z and no Unicode. Apr 5, 2022 at 21:21

R1 / (R1 + R2) is a ratio, a dimensionless number. The kohm part of the numerator and denominator cancel out each other. To see this, re-write

R1 + 10K

as

(R1 + 10) K

Because you have identical multipliers (k stands for x1000) in the numerator and denominator, they cancel out. As in some of the comments, if you replace every instance of k by x1000, your problem disappears.

Here is a hint: "kohms" = 1000 ohms

So any place you are seeing k, multiply what comes before it by 1000. So 20k becomes 20000, 6.67k becomes 6670, etc.

You're looking at an instance of dimensional analysis, where you carry along units to figure out what the units of your answer are.

The important thing isn't that you encounter the intermediate result of $$\V\cdot k\Omega\$$, which may or may not make any sense, but the the $$\k\Omega\$$ cancels out, leaving you with volts.

So, you know in advance that you're looking for an output of Volts, you carry along all your units in the analysis, cancel out what needs canceling out, and your remaining units are volts! Perfect! If, at the end, you don't get volts, you suspect that you made a mistake somewhere along the way, and you hunt it down and kill it.