Observations

# How does the length of the day vary from one day to the next throughout the year?

The change from one day to the next in the length of daylight durind 2011. Graph and calculation Nick Lomb

The length of the day is the interval between sunrise and sunset. We have discussed in a previous post how that varies during the year. Briefly, days are longest at the time of the summer solstice in December and the shortest at the winter solstice in June. At the two equinoxes in March and September the length of the day is about 12 hours, a mean value for the year.

Let us now ask what is the change in the day length from day-to-day? You may have noticed that the time of sunset since 2 January has not changed so far and will not change for a few more days until Friday 14 January 2011. The time of sunrise has been becoming later by about a minute each day so that the length of the day has been shortening accordingly.

The diagram above makes things clearer. The change from one day to the next at the time of the summer solstice in late December is around zero. Similarly, there is little change from day-to-day at the time of the winter solstice in June. This is not surprising as solstice means ‘the day the Sun stood still’, so at those two times of the year we expect little change from day-to-day.

There is more change at the time of the equinoxes – autumn and spring – in March and September respectively. At those times the changes day-to-day can be up to three minutes.

The curve above is surprisingly messy and not the smooth curve that would be expected. The probable explanation is that it is due to the rounding to the nearest minute in the calculation of sunrise and set times. If they were calculated to the nearest second then the curves calculated from them would be smoother. However, there is no point in giving sunrise and set times to any higher precision than a minute as atmospheric conditions each day can make the actual times vary slightly from the calculated times.

## 27 responses to “How does the length of the day vary from one day to the next throughout the year?”

• How many more minutes daytime in Hereford UK have my wife and I gained today since the solstice on 21st Dec 2019. Approx answer PLEASE

• Andrew Jacob says:

Peter, this is easy to estimate using the website time and date. Enter your location and navigate to the ‘Sunrise & Sunset’ page. There you will find tabulated the ‘daylength’. For your location – and as an example for anyone else to follow – the daylength on Jan 15 2020 was 8:15:12 [h:m:s] and on December 21 2019 daylength was 7:44:01. So you have gained 31min 11sec of daytime. In fact, it is only reasonable to estimate this time to the nearest minute because the actual time of sunrise is dependent on atmospheric refraction, your height above sea level and other effects. Also the the daytime gained is independent of the year, so will be the same next year.

• Cathy Bain says:

Is the amount of change in daylight even during a yearly cycle? It would seem to me that it would be even as the axis change alters at an even pace but charts make it look like a bell curve.

• Andrew Jacob says:

Cathy, Maybe I have misunderstood your question but the post makes clear that at the solstices the change in day-length is almost zero around the solstices and up to 3-minutes around the equinoxes.

• Ajay Karnik says:

Why The change in day length each day is more on higher lattitudes than at equator or tropics. I did not get satisfactory answer still by anyone

• Andrew Jacob says:

Ajay, I can answer this by considering the extremes of daytime length, i.e. sunrise to sunset. At the poles the daytime length varies from 0 to 24 hours per 24-hour day. In the tropics the daytime length varies by much less, for example at Rockhampton in Queensland, just on the Tropic of Capricorn it varies only from 10h42m up to 13h35m, a 2h53m diference (according to timeanddate.com). Since these changes in daytime length at both locations occur over exactly the same number of days during the year then at the poles the daily change in day length has to be greater there.
This is certainly the case around the equinoxes. However, around the times of the solstices the daily change in daytime length is close to zero for a few days everywhere.

• Rosemary Sharples says:

How do sunrise and sunset and twilight change from year to year? i’m interested in times in far north queensland in 1893. Are they basically the same every year? Would it be safe to say that the sun rose about 7 and set about 6 (18.00) then? Would twilight have been about the same? To be precise, the subjects of my article left Croydon in Qld on 16/7/1893 and cycled to Sydney, arriving 15/9/1893. They camped out a lot. They often started cycling about 6 a.m. Would they have been travelling in the dark? Would there be any sunlight?

• Andrew Jacob says:

Rosemary, Yes sunset, sunrise and twilight times remain basically the same, on the same calendar date, from year to year. There is a small cyclical shift of around half a minute that resets every four years, i.e. with the leap years, but that is insignificant in this context. However, over such a great distance (Croydon to Sydney) and time (July to September) the rise, set and twilight times may have been very different, you couldn’t say it rose at 7am every day of their journey. You could use an astronomy app or even time and date to determine if it was light or not each day when they started cycling. One imagines they would only have cycled when it was light enough. You might want to check the phases of the Moon too – maybe they could start earlier (or finish later) on some days if a nearly-full Moon was up.

• Ken Hunold says:

Hi Nick,

(If you’re still watching)

Even though there isn’t much reason to do so, there are ways to calculate sunrise times with greater precision. The NOAA website provides a spreadsheet that does just that. Using their spreadsheet, I plotted the change in length of day (in the USA) throughout 2019. At the very least, it makes your graph look better 🙂 .

I can’t attach my graph (it IS a smooth sine wave) but the NOAA spreadsheet is at:

https://www.esrl.noaa.gov/gmd/grad/solcalc/NOAA_Solar_Calculations_year.xls

Happy plotting!

• user says:

that sounds great! I think I will try this for in the uk. I was wondering if u could answer this or not but I am finding this website is not giving me my direct answer so may I ask u a question and get a reply/ answer? my question is why do the times when it is light or dark vary in length? it would be much needed if I could have a reply today however if not please do it at another possible time that is near this day of my reply. greatest thanks from me. sorry if I spelt anything wrong but I was in a rush.

• Andrew Jacob says:

user, You can use this TimeAndDate page to see how day and night length vary during the year (try jumping through the year in “+4 weeks” intervals). It is caused by the Earth being tilted, which leads to the seasonal changes in day-length and the change from winter to summer.

• Mike smith says:

Hi , can you tell me if daylight gains per day are split equally morning and evening? For example if we were gaing daylight at 3 mins per day , is that 1.5 morning 1.5 evening ? Or is it not equal ?
Thanks.
Mike

• Andrew Jacob says:

Mike, No, the gains (or losses) are not split equally. Once again this is due to the Equation of Time. You can use the spreadsheet in Ken’s comment below to investigate this.

• David MacLean says:

Can you help me understand how it is that around winter solstice, the change in sunrise time is less than the change in sunset time in the northern hemisphere? I fail to see how the changes would not be identical

• Andrew Jacob says:

David, this is caused by the effect of the Equation of Time. This defines the time when the Sun is due north, or equivalently the time of day exactly half way between sunrise and sunset. Read about the Equation of Time and the changes in sunrise/set times.

• James Gulick says:

The amount of daylight change day to day is the product of the earth’s poles’ tilt with respect to the sun— the same thing that gives us seasons. The best visual aid I can think of is a swinging pendulum. When it changes direction at each side analogous to the winter and summer solstices) the speed is lowest. But it picks up speed until it gets to the bottom of the swing (analogous to the vernal and fall equinoxes it is fastest). As the pendulum approaches the furthest point right or left it slows essentially to a stop when it changes direction. These ate cyclical motions.

• Nidhi says:

Winter solistic is in Dec and summer solistic is in june
Spring equinox is in march and autumn equinox is in September.
Some how article above is call ing it other way round??

• Andrew Jacob says:

Nidhi, Sydney Observatory is in the southern hemisphere. Down here things are the right way around 😉

• C says:

Depends on whether you’re in the northern or southern hemisphere.

• Andrew says:

I’m just wondering how day length occurs.

• Andrew Jacob says:

Andrew, I’m not quite sure what you are asking. As the post says a day (as opposed to a night) is the time between sunrise and sunset. Actually that’s a little ambiguous because we also define a ‘day’ as the time taken for Earth to rotate on its axis once. But you can find that definition anywhere, so have I misunderstood your question?

• Yomna ; ) says:

It occurs from sunrise to sunset and I also think that the Earth’s movement could be faster or slower.

A girl in grade 5.

• Ly Ching Nguan says:

Thank you for help me to understand it.

i;m still little confuse on it !OMG

• Terry VanHoozer says:

I have a basic grasp of the content above.

I don’t understand why the percentage of rate (day light) increases or decreases through out the year. Why isn’t it some sort of constant?
Speed of the planet in an elliptical orbit combined with the tile of the earth?

I live near the 47 parallel and the change is quite apparent over time. In watching the astronomic date on my weather channel I note that the daylight comes and goes at this different percentage at different times.

I’d appreciate some direction as to where to look next. I ask that you keep the vocabulary simple in that I have no degrees in this, simply a curiosity,
thank-you,
terry

• Doge says:

> You have to remember that the length of day light varies due to the 23.5 degree tilt that the Earth rotates on. Day length would always be equal if the Earth wasn’t tilted, but because it is, as the Earth travels around the sun, different parts of the planet will be tilted further towards (Summer time, which results in more daylight hours) or further away (Winter time, which results in more night time hours).
Speed of the planet is irrelevant here.
The picture on this may help: http://www.lpi.usra.edu/education/skytellers/day_night/about.shtml
However, it is contextualised towards America, so wherever you see a season, swap it in your mind for the opposite season.

• Andrew Jacob says:

We could look at this mathematically: this post displays the change-in-length-of-day which is the gradient or slope of the length-of-day plot shown in the previous post mentioned. The length-of-day plot is ‘cosinusoidal’ therefore its gradient plot is sinusoidal.

• Terry VanHoozer says:

Doge

Thanks for helping me understand what was right in front of me all the time.

In being an elliptical orbit around the sun, the velocity is not at a constant rate. Therefore what I’m viewing in the rate of change is an effect driven by this difference.
terry