How big is your Sleep Debt?

By Clinton Marquardt - Sleep & Fatigue Specialist

May 15, 2013

fatigue, jet-lag, shift-work, sleep tests

European moneyEveryone needs a certain amount of sleep every day. For most people this is between 7 and 8 hours. If you don’t get those 8 hours, a sleep debt can build up. When a sleep debt builds, the risk of fatigue and human performance problems increases.  It’s just like taking money out of your savings account without putting anything back in. The bigger the financial debt, the worse the problems.

I just did a quick on-line search for the term “Sleep Debt Calculator” and got 1,000’s of hits.  I tested a few of them and found they don’t all use the same formula.  Some overestimate and some underestimate.  The sleep debt formula I like to use is based on the idea that we need 8 hours of sleep per 24 hour day.  If we are sleeping for 8 hours, it means we are awake for 16 hours per day (8 + 16 = 24). This gives us a ratio of 1 hour of sleep for every 2 hours of wakefulness (1:2 or a factor of 0.5).

What I do, is I compare the amount of sleep obtained over a period of time to the amount of wakefulness over the same period of time divided by 2. I divide the wakefulness by 2 because this is the ratio of sleep to wakefulness.  Calculating the sleep debt this way takes into account the extra wakefulness that accumulates when sleep is missed.  For example, if you sleep for 7 hours instead of 8, the hour of missed sleep (8 – 7 = 1) is wakefulness and instead of being awake for 16 hours, you are awake for 17 hours in the 24 hour day.  I like this way of calculating sleep debt better than simply comparing the amount of sleep a person obtained to the amount of sleep they required because it makes more sense; if you are awake longer you become more fatigued and your sleep debt should be higher.

Here is the formula I use:

Sleep Debt = Total Sleep Time – (Total Awake Time x Ratio of Sleep to Wakefulness)

To keep it easy, I’ll illustrate the formula with a ratio of 1 sleep:2 wakefulness (i.e., 1/2 = 0.5) and a consistent bed time of 23:59.  If you need less than 8 or more than 8 hours of sleep, you can adjust the ratio.

Let’s say my sleep followed this pattern:

  • Friday Night = 5.5 hours starting at 23:59
  • Saturday Night = 6.5 hours starting at 23:59
  • Sunday Night = 7.5 hours starting at 23:59

Let’s also say that I am falling asleep at my desk at 14:00 Monday afternoon (no one does this right?) and I want to understand if my sleep debt is the reason.  So I calculate the amount of wakefulness that has accumulated since I went to sleep Friday night.  The starting point is important…wakefulness uses up sleep.  Remember the old video games that displayed an energy bar that slowly depleted over time?  It’s just like that with sleep except instead of energy, it’s often called a sleep reservoir. Always make sure you start your sleep debt calculation with a sleep period.

If I went to bed at 23:59 on Friday night and I got 5.5 hours of sleep, it means I was up at 05:30 on Saturday morning (we are all up by then on Saturday right?).  From 05:30 to 23:59 Saturday, 18.5 hours of wakefulness accumulate.  Sleeping for 6.5 hours on Saturday night and for 7.5 hours on Sunday night adds another 17.5 hours + 6.5 hours of wakefulness by the time 14:00 Monday afternoon rolls around. From Friday night to Monday afternoon, 42.5 hours of wakefulness and 19.5 hours of sleep accumulate. Applying the sleep debt formula gives:

Sleep Debt = 19.5 – (42.5 x 0.5) = – 1.75 hours of sleep debt

At 14:00 I have a sleep debt of almost 2 hours, that’s why I am falling asleep. If the result were a positive number, then no sleep debt would exist and I couldn’t blame my afternoon head nods on a lack of sleep.

There are much more complicated formulas out there, but this one provides a pretty good estimate of whether you are getting enough sleep.  The only caution I have is to keep in mind that you can’t put a whole bunch of sleep into your savings account and then withdraw it all in one long stretch.  You can’t sleep 15 hours a night four times and bank 60 hours of sleep and then take it all out at once. It’s unlikely you’ll ever come across this situation because we humans don’t work that way even if the sleep debt formula does. Just keep this caution in mind and you’ll be able to use the sleep debt formula to provide some decent estimates of whether someone is getting enough sleep.


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