Fixed in 13.0

On earth, the acceleration of free fall is around $9.81\,\text{m}/\text{s}^2$. In Mathematica,

g = Quantity["AccelerationOfFreeFall"]
(*    1 acceleration of free fall on the surface of the earth    *)

Converting to SI units gives a velocity ($\text{m}/\text{s}$) instead of an acceleration ($\text{m}/\text{s}^2$):

(*    (9.764 to 9.834) m/s    *)

(*    12.3.1 for Mac OS X x86 (64-bit) (June 19, 2021)    *)

A bug? Version-dependent?

  • $\begingroup$ No problem on 12.3.1 on windows 10. Screen shot !Mathematica graphics so looks like a bug that was fixed. $\endgroup$
    – Nasser
    Commented Nov 21, 2021 at 8:15
  • $\begingroup$ @Nasser you're looking at GravityAcceleration, which has no error bar but has the correct units. My question is about AccelerationOfFreeFall. $\endgroup$
    – Roman
    Commented Nov 21, 2021 at 8:26
  • $\begingroup$ This is strange. I swear I copied what you had there. I had no idea how it changed to GravityAcceleration. Must be some magic happened using the mouse. Ok, will try again: !Mathematica graphics so now it gives same as your on 12.3,1. Clearly this is a bug then. Oh, I remember now, I copied it from the posted answer, not from your question. The posted answer uses GravityAcceleration that is why. $\endgroup$
    – Nasser
    Commented Nov 21, 2021 at 8:33
  • 2
    $\begingroup$ This must be a mistake in their database. For example, it is also wrong in WolframAlpha: for the Basic unit dimensions it says $[\text{length}][\text{time}]^{-1}$. $\endgroup$
    – Domen
    Commented Nov 21, 2021 at 14:18
  • 1
    $\begingroup$ @kcr it's [CASE:4924593]. $\endgroup$
    – Roman
    Commented Mar 13, 2022 at 6:18

2 Answers 2


I get the same thing 12.0 for Windows which seems strange to me, but with

(*  196133/20000m/(s)^2  *)

(*  9.80665m/(s)^2  *)

"AccelerationOfFreeFall" does not appear to be generally compatible with UnitConvert; and when it does convert, it provides the wrong units.

{#, UnitConvert[Quantity["AccelerationOfFreeFall"], #]} & /@ 
  {"Conventional", "Imperial", "Metric", "SI", "SIBase"} // 
 Grid[#, Alignment -> Left] &

enter image description here

However, highlighting "GravityAcceleration" in Mathematica and pressing F1 for help, provides a link to StandardAtmosphereData. StandardAtmosphereData provides the correct units

StandardAtmosphereData[Quantity[0, "Meters"], "GravityAcceleration"]

(* Quantity[9.8066, ("Meters")/("Seconds")^2] *)

or with the various Methods

StandardAtmosphereData[Quantity[0, "Meters"], "GravityAcceleration", 
   Method -> #] & /@ {"Jacchia", "InternationalStandardAtmosphere", 

(* {Quantity[9.8066, ("Meters")/("Seconds")^2], 
 Quantity[9.8066, ("Meters")/("Seconds")^2], 
 Quantity[9.8066, ("Meters")/("Seconds")^2]} *)

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