How to calculate per second versus per minute billing?

December 15, 2005 4:04 PM

Telcos bill calls in varying minimum time increments (e.g. per second, per 6 seconds, per 30 seconds). Is there a formula to tell the difference this makes? Bonus points if it is on a web page or spreadsheet I can download.

I guess an even distribution of call lengths would need to be assumed, or perhaps it could take into account mean or median call duration?

posted by bystander to technology (8 comments total)

if they round to the nearest increment, on average it's a wash.

if they round up, as most probably do, and assuming the cost-per-minute is the same from one telco to the next:

take the per-minute charge and divide by 60 to get the per-second charge.

the number of seconds per call, modulo the billing increment, will be random. all call times within the increment are equally likely, so the amount you are overcharged is, in the limit of many calls, half of the increment * the number of calls * cost per second.
posted by sergeant sandwich at 4:14 PM on December 15, 2005

see also here.
posted by sergeant sandwich at 4:17 PM on December 15, 2005

To clarify, the increments round up, so a 35 second call is charged at 35x1/60th of the per minute rate with per second billing, or as 1 minute with 30 second billing. Clearly if the per minute charges are the same, the per second billing is favourable, but I am trying to compare varied rates.
Sergeant may be right, I will try and work through his explanation.
posted by bystander at 5:10 PM on December 15, 2005

sergeant sandwich: I think your theory falls apart on very short phone calls. My intuition is that calls that go to voicemail would skew the distribution way left.
posted by I Love Tacos at 5:14 PM on December 15, 2005

i love tacos: i think it's correct if most of the phone calls last longer than the minimum billing increment. if most of your phone calls are very short, you are right, the analysis is probably incorrect. it all depends on the user's calling habits, i guess.

some statistics are in order. here is a distribution of some phone call lengths, but the time scale is way off to be meaningfully useful. it's the only data i could find, though.

it seems to me that most phone calls that go directly to voice mail, are probably 5-10 seconds of ringing, a 10-15 second greeting, and another 10-15 second message left by the caller. if the range of billing increments is in the 6-30 second range, that puts you close enough to the minimum increment to be valid. ymmv!
posted by sergeant sandwich at 5:48 PM on December 15, 2005

bystander: if you want to compare different rates, just apply the equation above but with different per-second costs. i.e.

company A charges 3c/min in 15-second increments. the cost per second is 3c / 60 = .05 c. the average overcharge is then:
7.5 seconds * .05c / second = 0.375 cents per call.

company B charges 2c/min in 40-second increments. the cost per second is 2c / 60 = .033 c. the average overcharge is then:
20 seconds * .033c / second = 0.66 cents per call.

if you want to decide which is the better deal, you need to estimate how many phone calls you make and the total number of minutes they are. say you make 50 calls per month for a total of 350 minutes:

company A bill: 350 min * 3c/min = $10.50.
company B bill: 350 min * 2c/min = $7.00

company A overcharge: 50 calls * .375c = ~19 cents.
company B overcharge: 50 calls * .667c = ~33.35 cents.

so, you save about 11 cents per month going with company A, but it costs you 3.50 because of the higher per-minute charge. so, unless you make a LOT of very short phone calls, the incremental savings aren't going to make much of a difference.
posted by sergeant sandwich at 5:59 PM on December 15, 2005

Telecom can be such a dodgy field. Is it Sydney, Australia? A cursory glance of the telestra website suggests that local calls / long distance calls can be distant dependant. In the US Illinois and Wisconsin are shining examples of "farther away = more money" Here, we have local calls, they are band A, B, and C. Beyond that you are no longer intralata, but interlata, which can have a different billing rate altogether. Not to mention calling another state, etc. Really, you can make this as complicated or as simple as you want, you just have to establish baseline metrics / established call patterns.
posted by AllesKlar at 6:11 PM on December 15, 2005

If you have a uniform distribution of phone call lengths, ie your typical phone call is at least one billing increment then you will on average be overcharged by half of the billing increment.

To calculate the fraction you're overcharged by, just divide the average overcharge (eg 30s for 1-minute billing, 3s for 6s billing, etc) by your average phone call length.

The exception to the above is if your calls are short. My typical phone call length is 15-25 seconds so 1-minute billing would really suck for me.
posted by polyglot at 8:03 PM on December 15, 2005