Who needs this?
Acceleration turns up anywhere something speeds up, slows down or turns. A few groups deal with it regularly:
- Car peopleA spec sheet says 0–60 in 4.2 seconds, and a review says the car "pulls 0.7 g". Are those the same claim?
- Theme park fansA coaster brags about 4.5 g in the loop. That number has a physical meaning you can feel.
- Physics studentsKinematics problems mix m/s², ft/s² and g, sometimes in the same question.
- App and game developersPhone accelerometers report readings in m/s² or in g, depending on the platform.
- Pilots and drone flyersLoad limits on aircraft and gimbals are written in g's.
- Engineers and makersShipping, crash and vibration specs ("rated to 50 g shock") use the same unit.
Speed versus acceleration
Think of a car's speedometer. Speed is the number the needle points at. Acceleration is how quickly the needle is moving. A car cruising at a steady 70 mph has plenty of speed and zero acceleration. A car pulling away from a light at 5 mph has very little speed but may be accelerating hard.
That's why acceleration has the odd-looking unit "meters per second squared". It's really meters per second, per second: how many m/s of speed you add every second.
- m/s² is the SI unit. 3 m/s² means your speed grows by 3 m/s each second.
- ft/s² is the US customary version, common in older engineering and ballistics tables. 1 ft/s² is exactly 0.3048 m/s².
- g is acceleration compared with Earth's gravity. One g is the standard value 9.80665 m/s² (32.174 ft/s²). A car pulling 0.5 g is speeding up at half the rate a dropped rock does.
Slowing down is acceleration too, just in the opposite direction. Physicists don't need a separate word for it; drivers call it braking. Turning counts as well, because your direction changes even when the speedometer doesn't.
Doing the math, step by step
Turning a 0–60 time into g's
Work in meters and seconds, then divide by standard gravity. Here's a car that runs 0–60 mph in 6 seconds.
- Convert the speed
60 mph × 0.44704 = 26.8224 m/s - Divide by the time
26.8224 ÷ 6 = 4.4704 m/s² - Divide by g
4.4704 ÷ 9.80665 = 0.456 g
The same thing in feet
60 mph is exactly 88 ft/s, which makes the customary route almost as tidy.
- Convert the speed
60 mph = 88 ft/s - Divide by the time
88 ÷ 6 = 14.67 ft/s² - Divide by g
14.67 ÷ 32.174 = 0.456 g
Both routes land on the same answer, as they should. Keep in mind that this is the average over the run. Real cars pull harder in first gear and ease off as speed builds, so the peak figure is higher.
Real situations, worked out
26.8224 ÷ 3 = 8.94 m/s², and 8.94 ÷ 9.80665 = 0.91 g. That's close to the push of gravity itself, turned sideways and pressing you into the seat. It's about the same size as a hard emergency stop, just pointing the other way.
0–60 in 3 s ≈ 0.91 gA modern car on dry pavement can brake at roughly 0.8 to 1 g. At 0.8 g (7.85 m/s²) the stopping distance is 26.8224² ÷ (2 × 7.85) = 45.9 m, about 150 ft, and it takes about 3.4 seconds. At 1 g it's about 120 ft. That's braking distance only: at 60 mph you cover 88 ft every second before your foot even reaches the pedal.
60 mph to 0 at 0.8 g ≈ 150 ft of braking4 g means the seat pushes on you four times as hard as gravity normally does. A rider who weighs 150 lb feels like 600 lb for that moment, and arms suddenly feel very heavy. Big coasters usually peak somewhere around 3 to 5 g, and only for a second or two.
4 g on a 150 lb rider ≈ 600 lb of pushAnything falling freely near Earth's surface gains 9.80665 m/s every second, ignoring air. After 2 seconds that's 19.6 m/s (about 44 mph), and the phone has fallen 19.6 m (about 64 ft). Oddly, the phone's own accelerometer reads close to zero while it falls; the next section on mistakes explains why.
2 s of free fall ≈ 44 mph, 64 ftDoing it in your head
The handy peg: 1 g adds about 22 mph every second (exactly 21.94). So divide 60 by the 0–60 time to get mph per second, then divide by 22.
For metric, g ≈ 10 m/s² is close enough for most estimates; it's off by about 2%.
| 0–60 time | mph per second | Exact g | 60 ÷ time ÷ 22 | Off by |
|---|---|---|---|---|
| 3 s | 20 | 0.912 | 0.909 | 0.003 |
| 4 s | 15 | 0.684 | 0.682 | 0.002 |
| 5 s | 12 | 0.547 | 0.545 | 0.002 |
| 6 s | 10 | 0.456 | 0.455 | 0.001 |
| 8 s | 7.5 | 0.342 | 0.341 | 0.001 |
| 10 s | 6 | 0.274 | 0.273 | 0.001 |
What "5 g" feels like. g-force is a multiplier on how heavy you feel. At 2 g a 160 lb person feels like 320 lb; at 5 g, like 800 lb. Fighter pilots with g-suits and training handle around 9 g. Without that help, most people grey out well before that, so sustained high g is a job for professionals and their doctors, not a home experiment.
Common mistakes
Mixing up speed and acceleration. "This car does 0.5 g" says nothing about top speed. A loaded truck and a sports car can both cruise at 70 mph; what differs is how long it took them to get there. Speed has units like mph or m/s (speed guide); acceleration always has that extra "per second".
Forgetting to convert mph before dividing. 60 ÷ 6 = 10, but that's 10 mph per second, not 10 m/s². Divide by 9.80665 from there and you get 1.02 g, more than double the real 0.456 g. Get to m/s (or ft/s) first.
Thinking free fall is "1 g you can feel". In free fall you are accelerating at 1 g, but you feel weightless, because nothing is pushing back on you. What you feel as weight is the floor or seat pushing up. That's why a phone resting on a table reads about 9.8 m/s² and the same phone falling reads about 0. Astronauts on the space station feel weightless for the same reason: they're falling around Earth.
Treating g as a unit of force. The "g" in g-force is an acceleration. The force you feel is your mass times that acceleration, which is why the same 3 g feels heavier to a heavier person. The weight, mass and force guide untangles the pounds and newtons side of this.
A bit of history
- Early 1600sGalileo rolls balls down gently sloped ramps to slow falling motion enough to time it, and finds that distance grows with the square of time, the signature of steady acceleration.
- 1638Galileo publishes those results in Two New Sciences.
- 1687Isaac Newton's Principia sets out his laws of motion, tying force, mass and acceleration together (F = ma).
- 1901The 3rd General Conference on Weights and Measures (CGPM) adopts 9.80665 m/s² as the standard value of gravity, the "1 g" still used today.
- 1954US Air Force flight surgeon John Paul Stapp rides the rocket sled Sonic Wind to about 632 mph then is braked hard to a stop, taking a peak of about 46 g. His tests shaped seat belt and crash safety research.
Real gravity varies a little from place to place, slightly stronger at the poles and weaker on mountaintops. The 1901 value is a fixed reference so that "1 g" means the same thing everywhere.
Reference table
| g | m/s² | ft/s² | Roughly like |
|---|---|---|---|
| 0.1 | 0.981 | 3.22 | Gentle start in a loaded truck |
| 0.25 | 2.452 | 8.04 | 0–60 mph in about 11 s |
| 0.5 | 4.903 | 16.09 | 0–60 mph in about 5.5 s |
| 1 | 9.807 | 32.17 | Standard gravity; a very hard stop |
| 2 | 19.613 | 64.35 | A sharp coaster dip |
| 3 | 29.420 | 96.52 | Typical big coaster peak |
| 5 | 49.033 | 160.87 | Top end for coasters |
| 9 | 88.260 | 289.57 | Fighter pilot with a g-suit |
One m/s² is about 0.102 g, and one ft/s² is about 0.0311 g.
Questions people ask
How many m/s² is 1 g?
Exactly 9.80665 m/s² by definition, or about 32.174 ft/s². For quick estimates, 9.8 or even 10 m/s² is fine.
How do I convert a 0–60 time to g-force?
Divide 26.8224 (60 mph in m/s) by the time in seconds, then divide by 9.80665. Shortcut: 2.735 ÷ seconds. A 5-second car averages about 0.55 g.
Is deceleration different from acceleration?
Only in direction. Braking is acceleration pointing backward, and it uses the same units. A hard stop at 0.9 g is the same size of acceleration as a 0.9 g launch.
What g-force can a person survive?
It depends on direction, duration and support. Brief, well-restrained impacts like John Stapp's sled runs reached about 46 g, while sustained g in a fighter jet becomes a problem around 9 g even with a g-suit. For anything medical, ask a professional.
Why does my phone say 9.8 when it's sitting still?
The accelerometer measures the push from the table holding it up against gravity, which is about 1 g. Drop the phone and the reading falls to nearly zero, because nothing is pushing on it.