# Measurement in reciprocal metres

I'm trying to name a measurement that is measured in reciprocal length, which is in a draft document for vehicle risk management.

It currently says:

Crash rate = number of crashes / million kilometres driven


where the measurements are taken annually. So the units are in reciprocal length.

I'm not happy with the word "rate" because that seems to imply the number of events over time, whereas the measurement is the number of events over distance.

Existing names of units of reciprocal length in various disciplines don't seem to work - it's not a measurement of any cyclic phenomenon.

Is there an better word for this measurement?

• Usually, something that goes inverse to spatial measures and counts the presence of something is a density. e.g. linear density – alemi Jul 15 '14 at 16:15
• I don't really see such a strong link between "rate" and temporal phenomena. We happily use, for example, "exchange rate" for the number of dollars that you'll get for each euro, so I don't really see a problem in calling "the number of crashes you expect for each Mm" a rate. – Emilio Pisanty Jul 15 '14 at 16:20
• It's not so important which word you choose, as long as there is some fathomable relationship and you use it consistently. – Klik Jul 15 '14 at 16:43
• What about just frequency? It is a spatial frequency, as used in Fourier analysis for instance... But I have to agree with @EmilioPisanty here. – Anael Jul 15 '14 at 16:50
• @Anael Frequency is often (usually?) associated with things that occur regularly. It seem that johntait wants to avoid that implication. In a sense this is like the relationship between Hz = 1/s (cyclic) and Bq = 1/s (probabilistic). – dmckee --- ex-moderator kitten Jul 15 '14 at 23:57

I like alemi's suggestion in a comment of crash density, by analogy with the linear "mass density" for a rod.

Among other advantages, this frees up "crash rate" to mean the number of crashes per million hours driven.

Alternatively you could invert the crash density to talk about the "mean distance between crashes."

The term "Crash Recurrence" comes to mind.

http://dictionary.reference.com/browse/recurrence

1. an act or instance of recurring.