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In my May/June 2023 science article for The Magazine of Fantasy & Science Fiction I wrote about sundials: how they work and how to read one properly. In that article I promised to put up a web page on how to make your own sundial.

First, a link to the article: May/June F&SF Science Article. I suggest reading that first if you haven't already, but here's a quick recap of the important points:

Imagine the Earth out in space with the Sun off to the right. Stick a pole straight up at the North Pole and watch what its shadow does. In the spring and summer, when the Sun is above the horizon 24/7, the shadow makes a complete circle around the pole. If you put hour markers out at the end of the shadow's reach, you could tell time with it.

Now imagine that same pole down at 45° north latitude. It's casting the same shadow, but we've moved far enough around the curved surface of the Earth that the shadow falls on a slanted surface. However, to a person standing there next to the pole, the ground is flat and the pole is tilted. That's what a garden-style sundial, the kind most people are familiar with, looks like. Keep this concept in mind and sundials will make a lot more sense.

The basic idea behind a sundial is to have an object (the gnomon) cast a shadow on a graduated scale so as the Sun rises in the east and crosses the sky and sets in the west, the shadow of the gnomon sweeps around in a semicircle and hits a set of marks that tell you the time. The trick is to angle the gnomon properly and space the lines properly. (The gnomon's angle should match your latitude, so the top edge of the gnomon points at the north or south celestial pole.) In the early morning the Sun's shadow is long and moves more quickly than it does at noon, so the lines can't be spaced evenly all around the dial. (Well, they can, but that's on a different kind of sundial, which I'll explain below. On a flat "garden style" sundial, the lines aren't equally spaced.)

Before we get into how to make one, let's have a look at how NOT to make one. In the F&SF article, I explain how many (maybe even most) garden sundials are just decorative pieces of junk. Here's one such junk sundial in the photo at left. Notice how the hour lines don't point at the base of the gnomon (the triangular thing that casts the shadow). That means the shadow doesn't line up with the hour lines. You might try to read the time by noting where the shadow and the hour lines intersect at the perimeter of the dial, but the lines aren't spaced properly anyway. Notice how the six o'clock lines don't point at one another. How in the world is this sundial going to display the correct time when 6:00 a.m. isn't 12 hours away from 6:00 p.m.? Note also that the hours are divided into quarter-hour segments...except for 11:00 to 1:00. For some reason, there's no noon line. Worse, there's no noon gap, either. (We'll get to why you need one below.) Or rather, the manufacturer of this beautiful but useless sundial included a noon gap, but did it at the expense of the half hour between 11:45 and 12:15. Also, you can't tell from this photo but the gnomon is set at about a 30-degree angle. That's fine for the very southernmost parts of the US, but not for the area in which it was sold (Wyoming).

Oh, and the top of the gnomon isn't straight. The designer got carried away and made the decorative vines creep over the top, leaving bumps that create wiggles in the shadow.

This is the kind of sundial that kills people's interest in solar timekeeping, because no matter how you adjust its position, it will be wrong for every other time of the day. People think they just don't know how to read it properly, when in fact it's impossible to read the time on this sundial at all.

What this sundial tells you is that it's time to build a better sundial.

Here's a simple, easy sundial that's made from a sheet of 1/4" plywood, a length of 1/4" wooden dowel, and a corner cut off a plain 3/4" board. Note how the hour lines all point to the base of the gnomon. (Not the back of the wooden block, but to the spot where the upper edge of the wooden dowel would hit the plywood disk if it extended all the way down there on its own.) That means no matter where in the sky the Sun is, the shadow of the gnomon will fall along or next to a line, never crossing it.

I put the gnomon into a wooden block rather than directly into the plywood for two reasons: The plywood isn't thick enough to hold the gnomon securely, and the wooden block allowed me to fine-tune the gnomon's angle after I drilled the hole for it. I could sand the bottom of the block to raise or lower the tip of the gnomon until it was exactly at my latitude.

Note that the hour and minute lines are spaced farthest apart in the morning and evening, and narrowest at noon (except for the noon gap).

Notice the noon gap. It's the same width as the gnomon. That's because at noon you switch over from reading one side of the shadow to the other side, so you need to separate the morning and afternoon scales by the width of the gnomon.

The only difficult part of making this kind of sundial is drawing the lines. Their spacing is specific to your latitude. There are two ways to go about it. There's the mathematical way, which is fun if you're mathematically inclined, or there's the Internet, which has several sites that will calculate the angle of the lines for you based on your latitude.

My favorite site for the latter is Sundials.org. (This site will also tell you where you can find cool sundials near you. Check it out when you travel!)

Here's one that will draw the lines for you: Blocklayer.com

And in case those two sites disappear into the ozone, as websites are wont to do, here's another pretty good backup: Anycalculator.com

With any of these, just input your latitude and the site will calculate the angle (measured from Noon) that you need to draw the lines for every fifteen minute increment. Note that morning line angles are measured from the left-hand side of the noon gap and afternoon line angles are measured from the right-hand side of the noon gap. This is because you read the left-hand side of the gnomon's shadow before noon and the right-hand side after noon. (What you're really reading is the top of the gnomon.) People in the southern hemisphere should reverse just about everything: Point the dial at the south celestial pole and read morning times on the right side of the dial, using the right side of the shadow.

If you'd like to do the math yourself, the formula is fairly simple. It's tan(theta) = tan(HA) x sin(lat), where theta is the angle of the line you want to draw, HA is the hour angle of the Sun, and lat is the latitude where the sundial will be used. All angles are in degrees.

What's the hour angle? That's how many degrees away from solar noon the Sun is at the moment. So for 11:00 a.m. the sun is one hour away from noon. The Sun moves 360° in a day, and a day has 24 hours, so the sun moves 15° per hour. So the hour angle for 11:00 a.m. is -15°. It's minus because it's before noon.

So for a sundial at 45° latitude, our formula becomes tan(theta) = tan(-15) x sin(45). That reduces to tan(theta) = -0.1895, so theta is -10.73 degrees. So you would draw your 11:00 line 10.73 degrees to the left of your noon line.

Spreadsheet lovers, this is a classic example of a perfect spreadsheet problem. Go wild!

Here's what the lines should look like after you've drawn them, assuming you live at 45° North latitude. (You can add more hours for early morning and late evening as you wish.) The lines radiate from two points, the morning lines coming from the bottom left side of the noon gap and the afternoon lines coming from the bottom right side of the noon gap.

When you attach your gnomon, make sure the top edge of the gnomon points to the line between 6:00 a.m. and 6:00 p.m. You don't want the middle of the gnomon to go there, because the shadow of the gnomon at 6:00 would read 5:55 or so, and it would be off a decreasing amount all the way 'til noon. Remember: You're reading the shadow created by the top of the gnomon, so you want that part of the shadow to run down that 6:00 baseline.

With that in mind, you could easily make your gnomon a solid triangle, or a triangle with artsy cutouts. Anything will do as long as it has a straight top and you angle it at the same degree as your latitude. You measure the angle upward from the base, so a gnomon at 30° latitude would be fairly close to the dial, whereas a gnomon at 60 ° latitude would stand up closer to vertical. And of course at 90° latitude (the north or south poles) the gnomon would be vertical.

That's pretty much all you need to know in order to build a garden-style sundial. Draw the lines, attach a gnomon, and set it out in the sun. The gnomon has to point at the celestial pole. Fortunately for those of us in the northern hemisphere, the bright star Polaris marks that pole. So go out at night and aim the gnomon at Polaris. Or use a compass and calculate true north by adding or subtracting your magnetic declination from the compass reading. (You can find the magnetic declination for your home town on the Internet.)

One last caveat: The sundial has to be level in order to read properly. Which brings us to the next subject:

How to Read a Sundial

You might think that it's as simple as looking at the correct side of the shadow. Would that it were! Back in the days when sundials were in common use, it was. But when clocks were invented, we discovered something odd about sundials. They speed up during parts of the year and slow down during other parts of the year. That's right: The Sun doesn't keep accurate time! It's not the Sun's fault; it's a combination of two factors closer to home: the tilt of the Earth's axis and the eccentricity of the Earth's orbit. It's called the "analemma" correction, and the variation can be as much as 16 minutes, so it's important to do. The analemma correction makes for a neat graph. If you were to place a wide-angle camera in the same spot and take a picture at clock noon every day for a year, you would see that the Sun is low in the sky in the wintertime and high in the summer. You would also see it drift off to the left and the right due to the tilt of the Earth's axis and the eccentricity of our orbit. After a year's worth of exposures, you would wind up with a lopsided figure-8 traced out in the sky by the Sun.

This graph shows that figure-8, along with lines that tell you how fast or slow the Sun is running at different times of year. You'll see that there are four times of year when the correction is zero: a little before mid-June, at the beginning of September, right around Christmas, and about 2/3 of the way through April. Any other time of year requires a correction, which you can simply read off the graph.

There's another correcton for where you happen to be within your time zone. If you read the math part above, you'll remember that the Sun travels 15° across the sky per hour. So it should be no surprise that time zones are centered around 15° increments of longitude. The zero mark is the Prime Meridian in Greenwich, England, and we count in 15° increments around the globe to the west. So Iceland is one hour west at 15°, Greenland spans from 30° to 60° so they average it out as 45°, or -3 hours; North America runs from 60° to 120° and change (with Alaska extending all the way out to 165°) so it gets time zones from -4 to -8 hours, etc. But the Sun doesn't jerk along in 15° jumps; it slides smoothly along the sky. So when it's noon in Denver, Colorado, for instance, it's not quite noon yet a degree or two to the west. The Sun hasn't reached there yet. Which means a sundial in, say, Gunnison, Colorado will read a few minutes slow.

How many minutes? Well, if it takes the sun an hour to traverse 15° of sky, then it must take four minutes to traverse 1° of sky. (Four minutes is 1/15 of an hour.) So a sundial in Gunnison, which is 2° farther west than Denver, will read 8 minutes slow compared to one in Denver. But both towns are in the same time zone, so you have to add a correction factor to a Gunnison sundial to match one in Denver. I chose Denver because it’s right in the center of its time zone, so it requires no correction. But unless you’re also in the very center of your time zone, which would be 75° longitude for Eastern, 90° for Central, 105° for Mountain, 120° for Pacific, etc., you have to add or subtract a correction. That correction is +4 minutes for every degree west of center, and -4 minutes for every degree east of center. It can be as much as half an hour if you’re on the very edge of your time zone. Fortunately, once you know your correction, that never changes. (Unless you move.)

Plus there’s Daylight Saving Time. You have to add an hour for that when it’s in effect.

You might wonder why you can’t just move the sundial an hour ahead plus or minus your longitude correction. Wait for an accurate cloch to read noon, for instance, and set your sundial to also read noon, and you're done. Many people do that, but it throws off the time in the morning and the evening. It's tilting the pole away from true north. Your dial would run fast before noon and slow after noon.

So in order to read clock time off a sundial, you have to add and subtract those three correction factors:

1) Daylight Saving Time

2) Your position within your time zone

3) The daily analemma correction

Let's say we're looking at the sundial to the left, we're reading it on May 15th, and we're in my home town of Eugene, Oregon. The shadow reads 10:45 a.m. (Remember, we're reading the left side of the shadow before noon.) What do we do from here?

1) Daylight Saving Time is in effect, so we add an hour, to get 11:45.

2) Eugene is at 123° longitude, which means it's 3° west of the center of the Pacific time zone (120°). So Eugene's time zone correction is 12 minutes. And because we're west of center here and the Sun reaches the center of our time zone before it reaches Eugene, we have to add 12 minutes to the time above. That puts us at 11:57.

3) Reading the analemma graph for May 15th, you can see that the correction factor is -4 minutes. We have to subtract that from sundial time to get clock time. So we subtract 4 minutes from 11:57 to get 11:53. That's clock time as read off a sundial. (And we know it's 11:53 a.m. because the Sun wouldn't be shining in Eugene at 11:53 p.m!)

Whew! That's quite an involved process. Fortunately it becomes second nature within just a few readings. Check the time, factor in the corrections (one of which never changes and another of which only changes twice a year) and you've got it.

But isn't there another type of sundial that can be read directly? Yes, in fact, there is. It's called the Equatorial Sundial. Let's look at that next.

Equatorial Sundials

Let's imagine ourselves back at the North Pole again. Our gnomon is sticking straight up, and the Sun is circling around the sky, never setting. If we put up a fence around the pole and let the shadow land on the fence, we could use the fence for a sundial. And the cool thing about this sundial is that the numbers can be evenly spaced all the way around. That means if the fence was on a little train track, we could shift the whole fence around to account for our corrections. Move it forward an hour for Daylight Saving Time, move it back or forward for analemma time. (We don't have to worry about our longitude at the North Pole, because we're at every longitude at once!) We'd have to set the sundial for the analemma correction every day, but otherwise we could just leave it alone and read clock time directly off the scale.

Okay, now move that sundial to 45° North latitude. In order for the gnomon to point at the celestial pole, we now have to tilt it 45°, just as we had to tilt the gnomon on the garden-style sundial. But other than that, it works just the same. You can't read it at night because the Earth gets in the way of the sunlight, so the top half of the dial isn't necessary, but otherwise you can use it just as if it were at the North Pole. Give it a one-hour twist for Daylight Saving Time, give it another few minutes this way or that for your time zone correction, factor in the daily analemma correction, and you're good to go for the rest of the day.

There are dozens, probably hundreds, of ways to make an equatorial sundial. Here are two that I've built. The first is made from half-inch Baltic Birch plywood. I used a router to cut a circle 14" in diameter, then cut a 12" circle out of the center, leaving me with a 1" thick ring. I cut away most of one side, leaving about 2/3 of the ring. Then I calculated how many inches long the hour scale had to be per hour. That might sound tricky, but it's fairly easy. The circumference of a circle is just pi times the diameter, so for a 12" circle that's 37.7" in circumference. A full circle would be 24 hours, so divide 37.7" by 24 to get 1.57" per hour. I drew up a scale in Photoshop, printed it out in sections on a laser printer, cut it into strips, and stuck it to a cardboard backing made from a cereal box. I used double-stick tape to stick the scale to the inside of the circle.

The gnomon is a knitting needle donated by my wife, Kathy. It's suspended at the exact center of the circle on two wires that are wrapped around the ends of two wooden dowels slipped through snug holes drilled in the circle.

The scale and gnomon rest in a cradle of plywood blocks that hold the gnomon at the correct angle (my latitude) and let me slip the scale into place with whatever time mark I want at the very bottom. Bottom would be solar noon, so on May 15 in Eugene, Oregon I would set the dial one hour ahead for Daylight Saving Time, 12 more minutes ahead for my time zone correction, and minus four minutes for the analemma correction. That means I put 1:08 at the bottom on May 15th. Then I can read clock time directly for the rest of the day.

The larger equatorial sundial uses a 48" aluminum ruler bought at Harbor Freight Tools. I carefully bent it into a semicircle, using my hands and my knee and leaving it a little bit shy of a half circle. I then drilled holes at the ends and used wires to pull it into a semicircle so the wires would be under tension. I attached the gnomon (a bamboo barbecue skewer) to the wires, and did the same trick as above with calculating and printing the scale. (Alas, the lines already on the ruler weren't in the right places.) I rigged a different system for holding the ruler in place: a couple of wooden blocks for it to rest against and a metal hook that reaches over the top edge to secure it. The center of the hook becomes my bottom reference point. This big dial is accurate down to the minute.

Both sundials have leveling feet to allow me to level them on a slanted table. I need that capability because I take these sundials to my astronomy club's "Solar Sunday" star parties in one of our local parks, where we show people sunspots and prominences and stuff through solar-filtered telescopes and I show people how sundials work.

A word on gnomons for equatorial sundials: You want your gnomon to be long enough to cast a shadow on the dial at both midsummer and midwinter. Mine are a bit short, but they're loosely attached so I can scoot them upward or downward with the seasons. You also want your gnomon to cast a good shadow. It's tempting to make the gnomon really slender so it makes a razor-thin shadow, but that doesn't work. The Sun is half a degree wide in the sky, so shadows get smaller and fuzzier the farther away they are from the object that's casting them. Your gnomon needs to be big enough to cast a decent shadow. It can be really thick if you want, but if you make it that way you'll have to read one side of the shadow or the other throughout the day (no noon gaps on equatorial sundials). It's best to use a gnomon that casts a slender but distinct shadow so you can use the center of the shadow as your indicator.

If you want to make a 12" equatorial dial, or the larger one using a 48" ruler, I can save you the trouble of calculating and drawing the scales (although if you're into the math, you should do it yourself just for the fun of it!) Here are the print files:

Scale for small EQ sundial

12" EQ sundial scale.

Large EQ sundial scale

30.5" EQ sundial scale (which is the diameter you get with a 48" aluminum ruler bent into a half circle). This comes as two files:

FILE ONE: 6:00 - NOON

FILE TWO: NOON - 6:00

I made these to print on an HP Laserjet 4M, which has a very slight scaling factor (meaning an inch in Photoshop isn't quite an inch when it comes out of the printer). So you may have to re-scale these a bit for whatever printer you use, but this should at least save you the trouble of copying and pasting a bunch of lines. You have to cut out the printed sections and overlap the ends to make a continous scale. There's way more overlap than you need, but this way you don't have to be very precise with your cutting.

Mottos

Last, but not least, it's tradition for sundials to have mottos written on them, something to do with the passage of time. It can be a famous quote, a line from a poem or a song, or something you make up yourself. But if you want a fully traditional sundial, include a motto.

That's pretty much sundials in a nutshell. If you get interested in the subject, the Internet provides a bottomless rabbit hole of information on them. I've just scratched the surface here.

How to contact me

I'd love to hear from people who are interested in sundials. Please feel free to email me at the address on the right. (Sorry you can't click on it or copy and paste it; it's a graphic file to thwart spambots that search the internet for addresses to send junk mail to.) I have no idea how much mail this idea will generate, so I can't guarantee a response, but I'll do my best to answer everyone who writes with a genuine question or comment.