How fast can a signal go from Hyderabad to Washington, D.C.?

No faster than 44.28 ms one way and 88.56 ms there and back. That is light in a vacuum along the 13,274 km great circle between the two cities. Optical fibre slows light by its group index, 1.4682, so through glass the same round trip takes at least 130.02 ms.

The great circle from Hyderabad (17.42° N, 78.48° E) to Washington, D.C. (38.90° N, 77.10° W). Equal Earth projection; land from Natural Earth.

Floors from Hyderabad to Washington, D.C.
Medium	One way	Round trip
Light in a vacuum	44.28 ms	88.56 ms
Light in glass, group index 1.4682	65.01 ms	130.02 ms
Great-circle distance, WGS84	13,274 km

What does a real line add?

Cables leave the great circle, and every router and queue on the way adds time, so a measured round trip from Hyderabad to Washington, D.C. lands above 130.02 ms whenever the whole path is glass. A line that only just reaches 130.02 ms runs at 68.1 % of light, the most fibre allows.

Time Your Own LineYour connection, graded against light, from your browser

How are these floors computed?

The distance is Lambert's formula on the WGS84 ellipsoid between the population-weighted centres UN DESA gives for the two cities in World Urbanization Prospects 2025, checked against GeographicLib to within 100 m on ten pairs. Light covers 299,792.458 km each second. The glass figure uses Corning's group index for SMF-28e+ fibre at 1550 nm, 1.4682.