Volume is the easy part
Length times width times depth is arithmetic anyone can do. What these tools add is the part that decides whether the result was a good idea: the mix, the depth threshold, and the buffering.
The mix matters because a bed filled with pure compost drops by a quarter to a third in its first year as the organic matter decomposes, and holds water badly once it has dried out. Roughly half topsoil, a third compost and a fifth grit settles a little and then holds its level.
Depth matters because a mulch under about 25 mm does not suppress weeds at all — light still reaches the soil and it becomes a seed bed for whatever blows in. That threshold is roughly triple what most people actually spread.
And buffering matters because a single published liming rate is close to meaningless: clay resists a pH change nearly three times as hard as sand, so the same "kg per 100 m²" figure either does nothing or overshoots badly depending on which you have.
The order to do things in
Test the pH before you fill a bed rather than after. Lime takes months to act and sulphur needs warm soil and living bacteria before it does anything at all, so both are autumn jobs for a spring crop. Correcting the pH of a bed you have already planted is possible and much slower.
Then fill, then dress. Compost goes on the surface of an established bed rather than dug in — worms take it down within a season and the soil structure stays intact. Digging in is for breaking new ground and for backfilling a planting hole, not for annual maintenance.