# Thread: Need an equation for an energy Calculation

1. ## Need an equation for an energy Calculation

Money spent on gas = A (Dollars)

Night Time Unit rate = B (cents/KwH)

Day Time Unit Rate = C (cents/KwH)

The night time unit rate B is expressed as a % Y of the total Kwh for the money spent A

I need to know the number of KwH for B and C

For Clarity below I have shown an example of the reverse calculation

Total KwH (Z) 4702
Y% 55
Night Time KwH 2586.1 (Z*Y/100)
Night Time Unit Rate (B) 4.5
Night Time Money 116.3745 ((B/100)*(Z*Y/100))
Day Time KwH 2115.9 (Z*(100-Y)/100)
Day Time Unit Rate (C) 11.87
Day Time Money 251.15733 ((C/100)*(Z*(100-Y)/100))

This is a KwH to Money Conversion

I have been trying for a week now to come up with a formula for Money to KwH conversion

Thanks in advance for any help provided

2. Let $b= B/100$ and $c = C/100$. then

$Z = \frac{A}{bY+c(100-Y)}$

3. ## Problem Resolved

Thanks for that Badgerigar - your answer was actually incorrect but your thinking was spot on as it sent me down the right track.

The actual answer was

Z=((b*Y)+c*(100-Y))*A/100

Thanks it was in front of my nose all the time - long time out of high school

Thanks again

4. You can test formulas like these by taking a simple example. If we spend 4.5c on energy at night, the formula should give 1 kWh.

So A = 0.045, B = 4.5, C = 11.87, Y = 100.

b = 0.045 and c = 0.1187

Then plugging into your formula
Z=((0.045*100)+0.1187*(100-100))*0.045/100
entering this into a calculator gives
Z=0.002025
which is wrong, because 4.5c should have bought exactly one kWh.

checking my answer, I noticed that A was in dollars while B and C were in cents. This means my answer was also wrong. The correct formula should be

$Z = \frac{10 000A}{BY+C(100-Y)}$

Sorry to confuse you.