I changed to LED bulbs, and I wonder if it pays to buy a switch timer or if it is cheaper to leave it on at all times?
a "60W replacement" LED is usually around 10W actual.
10W * 12bulbs * 24 hours = 2880Watt-hours
2880Watt-hours = 2.88 kilowatt-hours
Your electric bill shows the price / kilowatt-hour. For me, with all applicable taxes and stuff, it's about $0.145 / kilowatt hour (I just paid my bill, so I have it right here)... yeah, that's 14.5 CENTS.
So every 24 hours those lights are on would cost me: 2.88 * 0.145 = $0.42
So if you were to use a timer to run them only 12 hours / day, you'd save $0.21 / day. If the timer costs $20, it would pay for itself after 100 days.
You will probably save money, but you have omitted several key pieces of information:
- What is the actual wattage of the bulbs? It's probably around 8-12 watts per bulb for a newer LED but it is easy to verify.
- How many hours will you save by using a timer?
- How many timers would you need to buy / how much do they cost?
- How much do you pay for electricity? In the USA that is measured in $ per kWh and is typically in the range of $0.08 to $0.25. As you can see there is a HUGE amount of variation even within the USA. Also note that rates can be different during day/night, and can also vary seasonally. You really need to find out what you pay to have any semblance of an accurate calculation... do not rely on the "national average".
CList gave the answer you're probably looking for and it was a great answer. (About $13 on your monthly bill to run them full time - so $6 savings per month)
I'll just add one thing however. It's NEVER cheaper to leave your lights on. Any amount of time that your lights are on, you're paying for it. What it comes down to, is how long you're willing to wait before considering it cheaper based on how many days you plan on running it for. You're not able to buy the $20 timer tonight and make back your money in savings by tomorrow, but you will save the money.
Say those 12 bulbs were incandescent (the power hogs that die quickly) and they draw 60 watts and only last about 50 days (12000 hours) running 24 hours. Just in one day you'd be running 17.28 kilowatt-hours of power, or (based on CList's example pricing) $2.51. By buying a timer in this case and running the lights for only 12 hours a day, you'd be saving $1.25 a day and easily make your money back in savings in just 16 days.
What I'm getting at is that you'll always save money by cutting the lights off. The bulbs will live longer and you'll be using much less electricity. It doesn't matter how efficient a bulb is, it's still using power when it's on. Thanks for reading.
The LED bulb packaging should list the power rating of the bulb like 10W or 5W or something. Once you know how much energy the bulb uses, it's a simple math problem of (X Watts * Y Hours) / 1000 = XY KW Hours. Then, from your electric bill you should be able to find a KW Hour price that you pay (say, 15 cents). Multiply the KW Hours used by the price you pay and that will be the electric cost of running the bulbs.
The other answers do a decent job of explaining the math behind figuring this out. However, there are assumptions being made that may not be completely correct regarding the actual watt-hour usage of an LED lamp.
Incandescent light bulbs are purely resistive, and therefore the voltage and current waveforms passing through them are in phase with each other, and the number of watts consumed is simply the voltage multiplied by the current.
However, LED bulbs are not resistive, but need to rectify the AC waveform and convert it to a DC voltage to drive the LED. This leads to voltage and current waveforms at the bulb that are not in phase. This results in some power being dissipated as "real power" and some as "reactive power".
Most watt-hour meters on houses (at least in the US, and this is changing because of non-linear loads like this) register only watt-hours (real power), and not VAR-hours (reactive power). The utility company may make some assumptions about your power usage and the types of loads on the circuit, and adjust their calculations accordingly.
Anyway, the point is you can probably ball-park this calculation, but you'll never know for sure, because the way the bulb uses power, the way your electric meter measures energy, and the way your utility calculates your bill all play a role.
I realize this doesn't quite answer the original question(s), but FYI.
My wife had five LED timed lights installed in the front garden to light up our home at night, until 1 AM. She reports that the electricity bill is virtually unchanged. So I installed "Bioluz" LED A19" bulbs throughout my home ($4.67 each in a 6-pack from Amazon), and my quarterly bill has noticeably dropped. The 60 w equivalent bulbs are said to last 10,000 hrs or about 10 years, so they more than pay for themselves.