# [ntp:questions] A question about the NTP delay time formula

Danny Mayer mayer at ntp.org
Wed Jun 24 03:28:30 UTC 2009

```Lei wrote:
> In RFC 2030(written by Prof. D.Mills), we have roundtrip delay time
> formula as follows:
>
>  d = (T4 - T1) - (T2 - T3) .................(1)
>
> However, IMHO, it should be
>
>  d = (T4-T1) - (T3 - T2)....................(1)'
>
> using which we can get
>
> t = ((T2 - T1) + (T3 - T4)) / 2 ...........(2)
>
> successfully by inserting d into the following formula
>
> t = T3 + d/2 - T4. ...........................(3)
>
> But if we use d as in formula (1), we can not get (2).
>
> Anyone has an idea? :)
>
> Thanks.
> -Lei

This was in error in the RFC. The NTP v4 draft shows it correctly
(Section 8):

The four most recent timestamps, T1 through T4, are used to compute
the offset of B relative to A

theta = T(B) - T(A) = 1/2 * [(T2-T1) + (T3-T4)]

and the round trip delay

delta = T(ABA) = (T4-T1) - (T3-T2).

Danny

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