20 Feet per Second in mph: Exact Conversion

This calculator converts a speed given in feet per second (ft/s) to miles per hour (mph). You enter the speed in feet per second, and it returns the equivalent speed in miles per hour, along with the underlying calculation. The conversion is exact and uses the standard relationship between feet, miles, seconds, and hours.

Formula

The conversion from feet per second to miles per hour is based on two fixed relationships: 1 mile = 5,280 feet, and 1 hour = 3,600 seconds. To convert, you divide the number of feet by the number of feet in a mile, and divide the number of seconds by the number of seconds in an hour.

mph = ft/s × (1 mile / 5,280 feet) × (3,600 seconds / 1 hour)

Simplifying the fraction 3,600 / 5,280 gives 0.681818… (repeating). So the practical formula is:

mph = ft/s × 0.681818

Where:

• ft/s = speed in feet per second
• mph = speed in miles per hour

Worked Example

Using the default value of 20 ft/s:

1. Start with the speed: 20 ft/s
2. Multiply by 0.681818: 20 × 0.681818 = 13.63636
3. Round to two decimal places: 13.64 mph

So 20 feet per second equals 13.64 miles per hour.

Why This Conversion Matters

Feet per second is common in engineering, physics, and sports (like baseball pitch speed or arrow velocity). Miles per hour is the standard for road speed in the US and UK. Converting between them is necessary when comparing measurements from different sources—for example, a wind speed reported in ft/s on a weather instrument versus a driving speed in mph.

This conversion is also useful for estimating stopping distances, conveyor belt speeds, or any moving object where the original measurement was taken in feet per second but you need to communicate it in miles per hour.

How to Read the Result

The result is a direct equivalent: if an object moves at 20 ft/s, it covers 20 feet every second. In mph, that same speed means it would cover 13.64 miles if it maintained that pace for one full hour. The number is always smaller in mph because one mile is much longer than one foot, and one hour is much longer than one second.

For quick mental estimates, you can multiply ft/s by 2/3 (0.667) to get a rough mph value. For 20 ft/s, that gives 13.3 mph—close to the exact 13.64. For precise work, use the full factor 0.681818.

Common Mistakes and Misconceptions

• Forgetting the 5,280 factor: Some people convert feet to miles (divide by 5,280) but forget to convert seconds to hours (multiply by 3,600). The combined factor is not 0.681818 if you skip one step.
• Reversing the conversion: To go from mph to ft/s, you multiply by 1.46667 (the reciprocal of 0.681818). Confusing the two directions is a common error.
• Rounding too early: If you round 0.681818 to 0.68, the result for 20 ft/s becomes 13.6 mph instead of 13.64. For large speeds, early rounding can cause noticeable errors.
• Assuming ft/s is the same as fps in gaming: In video games, “fps” usually means frames per second, not feet per second. This calculator is for physical speed, not frame rate.

Limits of the Formula

This conversion is exact and applies to any positive speed. There are no conditions or exceptions. However, the result is only as accurate as the input. If you measure speed with a stopwatch and a known distance, the uncertainty in your time measurement carries into the converted value. For example, a 0.1-second error over a 20-foot distance changes the speed by roughly 1 ft/s, which is about 0.68 mph.

The formula assumes a constant speed over the measured interval. If the object accelerates or decelerates, the ft/s value represents an average over that interval, and the mph result is that same average expressed in different units.

Practical Examples

• Baseball pitch: A 90 mph fastball is about 132 ft/s. Conversely, a 20 ft/s pitch would be a very slow 13.64 mph.
• Walking speed: A brisk walk is about 4 mph, which is roughly 5.87 ft/s. So 20 ft/s is more than three times faster than a typical walk.
• Conveyor belt: A belt moving at 20 ft/s transports items 20 feet down the line every second—about 13.64 mph, which is faster than most industrial belts.

Frequently Asked Questions

How do I convert mph back to ft/s?

Multiply the mph value by 1.46667 (which is 5,280 ÷ 3,600). For example, 13.64 mph × 1.46667 = 20 ft/s.

Is 20 ft/s fast?

It depends on context. For a human, 20 ft/s (13.64 mph) is a sprint—faster than most people can run for more than a few seconds. For a car, it’s a slow residential speed. For wind, it’s a moderate breeze (about 12 on the Beaufort scale).

Why is the conversion factor 0.681818 and not a round number?

Because 5,280 feet in a mile and 3,600 seconds in an hour do not divide evenly. The fraction 3,600/5,280 simplifies to 15/22, which is 0.681818… repeating. It’s a rational number with a repeating decimal, not a neat terminating one.

Can I use this for speed of sound or light?

Yes, but the numbers become very large. The speed of sound at sea level is about 1,126 ft/s, which is about 768 mph. The speed of light is about 983,571,056 ft/s, which is about 670,616,629 mph—the formula still works, just with huge inputs.

What is the difference between ft/s and fps?

In physics and engineering, ft/s and fps both mean feet per second. In computing, fps stands for frames per second (video frame rate). This calculator uses the physical meaning only.

Does this conversion work for negative speeds?

Yes, the formula is linear. A negative ft/s value (meaning motion in the opposite direction) converts to a negative mph value. The calculator allows negative inputs because speed can be directional.

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in fps | Speed | ft/s | 20 | 0
out mph | Speed | mph | fps * 0.681818 | 2