Which distance is more or less accurate can be known only through a case-by-case analysis. IRI & IR both use independent means of measuring distances. All other websites and publications are DERIVED from the Official Railways distances, and can be expected to reflect the exact same distances as in the official Railways publications. At this time, IRI is the only other source of independent railway distances.
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The Railways may use the actual odometer in locomotives to measure distances which are very accurate, except for cases of Distance Inflation in various track sections...
more... for differential calibration of Fares. For example, routes along Konkan are generally 40% distance inflated, to collect maintenance tolls. Besides that, section-wise distance inflations have been observed in the past near Dudhsagar Falls, CDG-UMB line, some bridge-crossings, etc. These may change from time to time, resulting in changing official distances between the same two stations!!! All of these may lead to generally larger Official Railway distances than shown in IRI.
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As for IRI, we use GPS-based distances along the routes shown in the Atlas. These are generally accurate to within 1 km. This small discrepancy is because the stations themselves may span more than a km in length. So, which part of station is taken for measuring distance may determine the final value. In the case of very long stations, the platform itself spans more than 1 km. If the Route is wrong or the station is misplotted, then the distances in IRI will also be wrong. We used to have several such cases earlier when the Atlas was new, but such instances have been reducing in frequency, but are still possible.
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As for correction of distances, we cannot manually correct distances in IRI. If the route in the IRI Atlas is wrong or if you observe that the corresponding stations have been misplotted in the Atlas, you may let us know. After the route is fixed, the distances will auto-correct themselves.
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If the stations are correctly plotted in the IRI Atlas and the Route also seems to be correct, and still there is a discrepancy, then it is upto your own judgment if you wish to consider the IRI distances.
Thanks.