Longer focal length magnifies the image, which also magnifies camera shake. To minimize blur from camera shake, 35 mm film format (size) has an old rule of thumb that hand-held shutter speed should be at least:
If a 200 mm lens, then at least 1/200 second shutter.
But for sensors smaller than 35 mm film, this would be
If 1.5x crop and 200 mm lens, then at least 1/300 second shutter.
This about crop factor is because the same viewing size must enlarge a smaller image that much more. People vary in their ability to hand-hold the camera still enough, so this is a little crude, and at least doubling this shutter speed is not a bad idea. If pondering why your images are not sharp enough, check the shutter speed in the Exif. Using a speedlight flash can also be a big help to freeze any motion. We should always be thinking about reducing camera shake.
If you don't know sensor dimensions, the second megapixel choice will compute them.
I'm just playing with the subject of camera shake. The calculator is accurate, but it's just a novelty, not really numerically useful since we don't have numbers for how much camera shake there was. The point it hopes to make is about realizing that slight camera shake can have significant effect at the sensor. A faster shutter speed can help freeze it.
Greater focal length magnifies motion at the sensor, but greater distance reduces it. Half the distance is seen at the camera as twice the motion, but twice the distance is half the motion (as seen at the camera). A plane flying 450 miles per hour at 25000 feet has only minimal motion blur (comparable to DOF CoC limits) in a 200 mm lens at 1/250 second. But a car at 30 miles per hour at 25 feet has extremely more blur.
Subject motion speed can be calculated, in pixels of blur. Subject motion sideways across the camera has the maximum computed effect. Subject motion at 45 degrees to the lens axis has about 70% effect. Subject motion directly towards or away from the camera is just a size difference, but which as "motion" will have relatively little effect during shutter speed duration (meaning twice the shutter time is twice the sideways motion, but twice the time forward is NOT half of the camera distance, depending on an extremely close distance maybe, but it is generally much less perceptible as motion).
You can enter a guess of how much motion might occur (how much the subject image moves out at the distance), or a second option will compute a subject motion of a motion speed rate for a duration (shutter speed). The default "1/16 inch" shown is to be the blur motion at the subject, which we might be able to guess at in the picture. I realize we may not know those numbers, but it might be fun to play with, to get an idea about the effect of motion (the specific goal is to actually realize how much it matters). We should always be thinking about reducing camera shake.
Do note the default case shown, that with a 105 mm lens, camera shake that moves the subject image 1/16 inch at 10 feet (0.0298 degrees) is 14 pixels of blur on this default sensor. Tricky here, but that current default of 1/16 inch motion is specified as 1/16 inch movement regardless of shutter speed. At the current Duration shutter speed, 1/16 inch motion is computed to be 1.302 ft/sec speed of motion. Then using that speed, the durations will compute the same movement speed for other shutter speeds i.e., double shutter speed will be half the shake).
The comparison to CoC is in reference to Depth of Field standards. The blur circle at the extremes of allowable Depth of Field distance is called Circle of Confusion (CoC). CoC is the largest blur considered minimally but perhaps acceptably sharp in Depth of Field considerations. Motion blur is not related to focus, but CoC is an existing standard of sharpness, and it is used a size reference here. Blur computed to be 2.78x CoC is 2.78 times larger than the maximum that Depth of Field would call minimally acceptable. CoC is discussed more with the DOF calculator here .
We do have a rough general rule of thumb about the necessary handheld shutter speed that will usually freeze typical motion in continuous light (like daylight or incandescent). It specifies that the shutter speed should be at least 1 / Focal length as seconds, for example, 1/100 second minimum shutter speed for focal length 100 mm. That was the rule for 35 mm film, and for digital, it should be 1 / Equivalent Focal length (focal length x crop factor, or 1/150 second for crop factor 1.5 with the 100 mm lens in this example). It is only a rough guide, because people vary in what they can reliably hand hold steady. Some may hold steadier, and some are worse. "Thinking" about holding it steady during the exposure always seems a big help. Camera image stabilization methods (Nikon VR, Canon IS) help hand holding with slow shutter speeds (allowing up to two or three stops slower), but it has no effect on subject movement. Tripods are good for camera shake, and speedlight flash is good for any motion.
One advantage (of several) of the speedlight flash is that its light duration is very fast (for example, maybe 1/2700 second if at 1/4 power level), where the shutter speed might be 1/60 to 1/200 second (perhaps 45 to 13 times longer illumination for the motion to blur things). And much faster at lower power levels (for close up work). The speedlight flash can be fantastic for stopping motion, either subject motion or camera shake (like for macro work, handheld in the field). See more about use for High Speed Flash Photography.