# Is there a linear relationship between shutter speed and speed of subject to freeze motion?

Is there a calculation that I can do that will calculate the required shutter speed if I know the speed of my subject and want to get a crisp image e.g. freeze motion?

For example if I go to a car race and focus on a particular corner, where I know the max speed of the cars - is there a calculation I can do to work out my shutter speed before I setup?

Or if I know the speed at which the Earth rotates can I devise a perfect shutter speed to freeze the moon?

Would be amazing if you could devise an optimum shutter speed per subject chart, like a shutter speed cheat-sheet?

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I think the problem with a cheat sheet is that the situations where all the variables are known within enough tolerance to be useful are rare. – mattdm Apr 15 '12 at 12:21
You're right, mattdm. However, most of the variables do not need to be known. If you gauge subject speed (relative to the camera) in terms of how long it might take to cross the field of view, you arrive at an extremely simple solution: divide that time by the length of the sensor in pixels to obtain an exposure duration that will cause less than one pixel of blur. Adjust that answer to meet your personal standards of sharpness (and to match the lens's sharpness). The formula is so simple, and so little needs to be memorized (sensor size), that this works well in the field. – whuber Apr 15 '12 at 14:29
@whuber Most 'rules of thumb' are based on the assumption of standard viewing: An 8x10 inch print viewed at a distance of 10 inches by a person with 20/20 vision. This allows a lot more leeway than a single pixel standard. When viewed at 100% on a 72ppi monitor a 6000x4000 pixel (24MP) image is enlarged to the equivalent display size of 83x56 inches! Even if you double the viewing distance to 20 inches, that's still the size of a 42x28 inch print. – Michael Clark Sep 10 '13 at 19:51
Thanks, @Michael, for expanding on the meaning of personal standards of sharpness. Because many (most?) photographs are rarely framed exactly right, they need cropping, so do not forget to take that into account. (I would love to have your 6000x4000 monitor, by the way. But my collection of monitors is such that there often is a 1:1 relationship between pixels in the cropped area and pixels on the monitors, so the one-pixel-of-blur standard is a meaningful, if somewhat stringent, reference for me.) – whuber Sep 10 '13 at 20:13
Generally speaking, viewing an image at 100% means viewing a portion of the image so that each pixel in the image is displayed as one pixel on the monitor. It doesn't mean viewing the entire image remapped to the monitor's native resolution. If you are cropping a typical 20MP image to fit on a typical HD monitor (2MP), you're doing much more than just adjusting the edges for fine-tuning the original framing, you are zooming by a factor of about 3. – Michael Clark Sep 10 '13 at 20:20

Shutter speed can be calculated - all you have to do it calculate the time it takes the subject to move one pixel in the image.

Unsurprisingly, other people already made those calculators, there's one here and another here

I've even seen a cheat sheet like you want but I can't find it right now (I was sure I bookmarked it)

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@Nir has the basic, how many pixels can you tolerate being blurred. Your example parts are actually bad examples. The moon is in direct daylight, so its bright and you typically shoot at F5.6 with a fast shutter speed. For race cars, you never want to freeze motion, they will look like museum pieces. You typically use a slow speed and pan to show the motion. – Pat Farrell Apr 15 '12 at 16:27
Would love to see that cheat sheet if you find it – Rob Apr 15 '12 at 17:45
@Rob - I just can't find it, if I find it in the future I'll link to it from my answer – Nir Apr 15 '12 at 21:04

I did some math and came up with this:

t = 3.6 * N * d * s / (v * f * res_x)

where

• t ... time [s]
• N ... number of pixels
• d ... distance between object and focal plane [m]
• s ... horizontal size of sensor [mm]
• v ... object speed [km/h]
• f ... focal length [mm]
• res_x ... horizontal resolution of sensor

N means how many pixels you will tolerate the object to be "smudged" over. It is the maximum distance in pixels you want to allow the object to move on your image.

## An example

Let's assume I have a fullframe camera with a 50mm lens, and I am taking a photo of a walking person, who moves perpendicular to me (at a speed of 5 km/h) and is 10 meters distant. I tolerate movement on the image by 8 pixels. My photos are 4288x2848.

t = 3.6 * 8 * 10 * 36 / (5 * 50 * 4288) = 0.00967 [s]
t = (1 / 103) [s]

Note:

I assume I have a tripod and the camera doesn't move. Otherwise, you will have to recompute the speed of the object relative to your camera.

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Oh my, the grammar was really awful. Thanks for edit :) – Petr Újezdský Apr 15 '12 at 13:38
I believe d is actually the distance between the object and the focal plane, not the object and lens. – Dan Wolfgang Apr 15 '12 at 20:28
You are right, I have corrected it. – Petr Újezdský Apr 15 '12 at 21:34

While it's possible to reduce this to a calculation, I question how valuable it would be. I don't think most people are going to be accurate enough at estimating subject distance and exact speed in order to be able to pull this off.

Instead, I think you would learn from experience much faster. If nothing else, bring something like a Hoodman loupe along, and chimp your photos with several different shutter speeds.

Even once you figure out exactly how fast to freeze a race car, you'll then get into an aesthetic issue of making it look nice. Frozen helicopter blades and frozen tires aren't necessarily the best way to capture the feeling. :)

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Agreed. Plus, how long is it going to take to do the math and how quickly is the subject moving? By the time you estimate the subject distance and speed, check your focal length (if you're using a zoom), and actually do the math (and you'll almost definitely need a calculator to plug such specific numbers in), the subject will have moved -- and perhaps even passed you! Learning from experience will be much easier, I think! – Dan Wolfgang Apr 15 '12 at 20:31
and you might also move the camera with the subject to keep it still, while the background blurs. – Michael Nielsen Sep 22 '12 at 17:43