Feet per Second Squared to mph: Conversion Guide

This calculator converts an acceleration value from feet per second squared (ft/s²) to miles per hour per second (mph/s) and also shows the equivalent change in speed over one minute. You enter the acceleration in ft/s², and the calculator returns the corresponding rate of speed change in mph/s, plus the total speed gain after 60 seconds. The conversion is a straightforward unit change, not a physical transformation.

Formula

The core conversion factor comes from the relationship between feet, miles, and seconds:

1 mile = 5280 feet
1 hour = 3600 seconds

Therefore, 1 ft/s = (1/5280) miles / (1/3600) hours = 3600/5280 mph = 0.681818 mph.

For acceleration (ft/s²), you are changing speed by a certain number of ft/s every second. Multiply that by 0.681818 to get the change in mph per second:

mph/s = ft/s² × 0.681818

Where:

• ft/s² – acceleration in feet per second squared (the input)
• mph/s – the equivalent rate of speed change in miles per hour per second (the output)
• 0.681818 – the exact conversion factor (3600/5280)

To get the speed change after one minute, multiply the mph/s value by 60.

Worked Example

Using the default value of 32.174 ft/s² (standard gravity):

1. Start with the acceleration: 32.174 ft/s²
2. Multiply by the conversion factor: 32.174 × 0.681818 = 21.936 mph/s
3. So the speed increases by about 21.94 mph every second.
4. After 60 seconds (one minute), the total speed gain would be 21.936 × 60 = 1316.16 mph/min.

This matches the calculator output: 21.94 mph/s and 1316.16 mph/min.

Why This Conversion Matters

Acceleration is often quoted in ft/s² in physics and engineering textbooks, especially in the United States. However, most people have an intuitive feel for miles per hour, not feet per second. When a car advertisement says “0 to 60 in 5 seconds,” that’s an average acceleration of 12 mph/s (about 17.6 ft/s²). Converting between these units lets you compare accelerations across different contexts—car specs, roller coaster forces, or physics problems.

The conversion is also useful in accident reconstruction and vehicle testing, where engineers record deceleration in ft/s² but need to express it in terms a jury or client understands (like “the car slowed from 60 mph to 0 in 4 seconds”).

How to Do the Conversion Manually

If you don’t have the calculator handy, the process is simple:

1. Take the acceleration value in ft/s².
2. Multiply by 0.681818 to get mph/s.
3. If you want the speed change over a specific time (t seconds), multiply the mph/s value by t.

For example, an acceleration of 10 ft/s² is:

• 10 × 0.681818 = 6.82 mph/s
• After 3 seconds: 6.82 × 3 = 20.45 mph
• After 10 seconds: 6.82 × 10 = 68.18 mph

This works for deceleration too—just use a negative value.

Common Mistakes and Misconceptions

One frequent error is mixing up ft/s² with ft/s. The former is acceleration (change in speed per second), the latter is speed. Another mistake is forgetting that the conversion factor applies to the whole unit—you’re converting ft/s to mph, not just feet to miles. Also, some people mistakenly multiply by 0.681818 twice, thinking they need to convert the squared second as well. That’s wrong: the “per second” part stays the same because the time unit in the denominator is already seconds.

Another misconception is that “mph per second” is the same as “mph squared.” It isn’t. mph/s is a perfectly valid unit of acceleration, while mph² has no physical meaning in this context.

Practical Examples from Everyday Life

Here are some real-world accelerations to give you a sense of scale:

• Elevator start/stop: roughly 4–6 ft/s² (2.7–4.1 mph/s)
• Sports car 0–60 in 4 seconds: average 22 ft/s² (15 mph/s)
• Passenger jet takeoff: about 10–12 ft/s² (6.8–8.2 mph/s)
• Hard braking in a car: about 20 ft/s² (13.6 mph/s)
• Standard gravity: 32.174 ft/s² (21.94 mph/s)

These numbers help you judge whether a given acceleration is gentle, moderate, or extreme.

Limits of the Conversion

This conversion is purely mathematical—it doesn’t account for real-world factors like air resistance, friction, or engine power curves. A car’s acceleration isn’t constant; it decreases as speed increases. So a single ft/s² value represents an instantaneous acceleration, not an average over a whole run. When you see “0–60 in 5 seconds,” that’s an average, not a constant acceleration.

Also note that the conversion factor is exact (3600/5280), but rounding to 0.681818 introduces a tiny error (about 0.0002%). For most purposes, that’s negligible.

Frequently Asked Questions

How many mph/s is 1 ft/s²?

Exactly 0.681818 mph/s. That’s because 1 ft/s equals 0.681818 mph, and the acceleration unit means you gain that much speed each second.

What’s the difference between ft/s² and mph/s?

They’re both units of acceleration—just different measurement systems. ft/s² is the standard unit in physics (imperial), mph/s is more intuitive for vehicle performance. The conversion factor is constant: 1 ft/s² = 0.681818 mph/s.

Can I convert ft/s² to mph directly without the “per second”?

No. ft/s² is acceleration, mph is speed. You need a time interval to convert an acceleration into a speed change. For example, 10 ft/s² over 5 seconds gives a speed change of 34.09 mph (10 × 0.681818 × 5).

Why is the conversion factor 0.681818?

Because there are 5280 feet in a mile and 3600 seconds in an hour. So 1 ft/s = (1/5280) miles per (1/3600) hours = 3600/5280 = 0.681818 mph. The same factor applies to acceleration.

Is 32.174 ft/s² the same as 1 g?

Yes, 32.174 ft/s² is the standard acceleration due to gravity at Earth’s surface. In mph/s, that’s 21.94 mph/s—meaning if you fell freely, your speed would increase by about 22 mph every second (ignoring air resistance).

How do I convert mph/s back to ft/s²?

Divide by 0.681818, or multiply by 1.46667 (the reciprocal). For example, 10 mph/s ÷ 0.681818 = 14.67 ft/s².

Related

• Power and Efficiency Formula: How to Calculate
• 70 mph to Feet per Second: Exact Speed
• Multiplying Negative Fractions: Rules & Examples

in a | Acceleration | ft/s² | 32.174 | 0
out mphs | Speed change per second | mph/s | a * 0.681818 | 2
out mphmin | Speed change per minute | mph/min | a * 40.9091 | 2