Phew, that loop on the rollercoaster pulled a whole 5 g: let the adrenaline go and learn what it means with our g force calculator.

In this short article, you will learn:

  • What is gravity, and how to calculate the gravitational force on the surface of Earth;
  • How to calculate the g force acceleration: how much is a 1 g force;
  • How to measure acceleration in terms of the g force: equation and formula for the g force; and
  • What the relationship between g force and speed is.

A few words about gravity

Gravity is a fundamental force existing between massive (and energetic) bodies, characterized by:

  • Long-range action;
  • Weak strength; and
  • Mysterious carriers.

With these three features, we compare gravity to the other fundamental forces (weak and strong nuclear and electromagnetic forces). While the others act primarily at the atomic scale (or slightly above it), gravity dominates our daily experiences and absolutely dwarfs all the others at the astronomic scale. On the other hand, gravity is weak: to feel its effect, you have to be massive.

🙋 We intuitively know this! Gravity tends to be less harsh toward small objects. The damages resulting from a fall differ enormously from a human being to a squirrel.

While we know the carriers for the other forces (all elementary particles), scientists still have no clue about the nature of gravity. While they suspect the existence of a particle called gluon, it is nowhere to be found yet!

How to calculate the gravitational force

We need to thank the OG nerd Isaac Newton for the mathematical expression of gravity. Not by observing falling apples but by studying, the scientist developed the equation we still use to calculate the gravitational force:

F=Gm1m2r2F = G \cdot \frac{m_1\cdot m_2}{r^2}

Where:

  • GG is the gravitational constant, a (suspected) universal constant;
  • m1m_1 is the mass of the first body;
  • m2m_2 is the mass of the second body; and
  • rr is the **distance **between the centers of the two bodies.

Newton comes in our help again: by applying Newton's second law, we can calculate the acceleration due to gravity:

F=Gm1r2F = G \cdot \frac{m_1}{r^2}

We simply canceled out the mass of the "attracted body".

On Earth, this acceleration is easily calculated: plug the value of Earth's mass and the average Earth's radius:

a=6.6743 m3kg ⁣ ⁣s2 ⁣ ⁣5.972 ⁣ ⁣1024 kg6, ⁣371, ⁣000 m=9.82 ms2\begin{align*} a& = 6.6743\ \frac{\text{m}^3}{\text{kg}\!\cdot\!\text{s}^2}\! \cdot \!\frac{5.972\!\cdot\!10^{24}\ \text{kg}}{6,\!371,\!000\ \text{m}}\\ \\ &= 9.82\ \frac{\text{m}}{\text{s}^2} \end{align*}

This value must be familiar: this is the acceleration with which every object (neglecting air resistance) falls. It is also a good metric to measure accelerations, particularly in vehicles. Let's find out more!

How much is a 1 g force? Accelerations in terms of gravity

An acceleration of 9.82 m/s29.82\ \text{m}/\text{s}^2 is the answer to the question "how much is a 1 g force". Living on Earth, our daily lives are constantly subjected to 1 g1\ \text{g} acceleration so that we don't really notice. Actually, it's easier to notice when there are changes to this "status quo".

When you take the elevator (or the lift, if you went to buy tea), you can feel that funny sensation in your belly: that's the effect of a vertical acceleration that adds (if you are going up) or subtracts (if you are going down) to the g force acceleration. The same thing happens when you are taking off on a plane or you take a speed bump just a bit too fast in a car: it feels strange because humans are not used to moving vertically!

A reasonable value for the acceleration of an elevator is 1.2 m/s21.2\ \text{m}/\text{s}^2. This is about an eighth of the value of the gravitational acceleration on Earth's surface. We feel this variation. The same acceleration would bring your car from 00 to 60 mph60\ \text{mph} (100 km/h100\ \text{km}/\text{h}) in slightly more than 2020 seconds. Not that impressive, right?

In the next section, we will learn how to calculate any acceleration in g.

Calculate the g force: equation to find the acceleration in g

Say that you want to calculate the g force, or, in other words, how many g that acceleration was: you can use the g force formula to do so:

g Force=vfvitg=Δvtg=agg\ \text{Force} = \frac{v_{\text{f}}-v_{\text{i}}}{t\cdot g}=\frac{\Delta v}{t \cdot g}=\frac{a}{g}

Where:

  • vfv_{\text{f}} and viv_{\text{i}} are the final and initial velocity, that define the Δv\Delta v (difference in velocity: don't mistake it with the delta v of a rocket);
  • tt is the time elapsed between the initial and final moments; and
  • aa is the acceleration.

The result of the equation allows you to calculate the g force from the speed, given that you know the time required to reach that value. Remember: gg is an acceleration, not a velocity: you can't readily compare the two quantities.

When too much is too much: the limits of the g force acceleration

Humans are pretty strong: we can sustain a relatively high number of g and get up to tell others about our experiences. Daily, we rarely exceed accelerations higher than a few fractions of g. However, we may reach higher values when we lift our feet from the ground.

🙋 When you are in a free fall, you are accelerating at exactly (or slightly less than, if the air is in the way) 1 g1\ g. During these moments, you are experiencing no contact forces, and all of your body is subjected to the same force. You are accelerating at 9.81 m/s29.81\ \text{m}/\text{s}^2 too, even if you are standing, but the floor is pushing against you with what you perceive as "weight"!

When you take off, on your way to your holidays, you experience, on average, 0.4 g0.4\ g: that's almost half more than what you're used to, and you will feel it: in that short moment, your perceived weight increase: from, say, 70 kg70\ \text{kg}, you would feel, for a moment, as if you weighted almost 100 kg100\ \text{kg}!

On a roller coaster, you can easily experience accelerations up to 5 g5\ g, luckily for short periods of time. Earlier, less-engineered models pushed this number a bit further by mistake: the passenger on the rides would be subjected to accelerations reaching 12 g12\ g. Do you know who else experiences such accelerations? Fighter jet pilots, and only the best ones don't pass out doing so. Beyond 9 g9\ g-12 g12\ g, the risk of severe injuries increases. The current record for the highest g forces experienced by a human is 214g214 g, sustained by Kenny Bräck in a racecar crash. More notorious, though by far less strong, are the experiments of John Stapp on rocket-powered sleds. The researcher voluntarily pulled an impressive 46.2g46.2 g without injuries and ended up saying that he thought that humans could sustain much more than that!

Davide Borchia
Gravitational acceleration
Mass (M)
Earths
Distance (r)
ft
Gravitational constant (G)
x10⁻¹¹
m³/kg⋅s²
Acceleration due to gravity (g)
ft/s²
Linear motion
Initial velocity (V₀)
ft/s
Final velocity (V₁)
Time (t)
sec
Gravitational force equivalent (F)
g
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