upward, upwards
1. The only form for the adjective is upward (in an upward direction), but upward and upwards are both used for the adverb, with a preference for upwards in BrE:

• The launcher consists of a small nozzle that directs a jet of water upward at an angle of approximately 45 degrees —Scientific American, 1973

• James had rounded off sums downwards rather than upwards —writing £900 for an actual £975 for example —K. M. E. Murray, 1977.

2. Upwards of (or occasionally upward of) is first recorded in the early 18c in the meaning ‘rather more than’ and remains in standard use:

• British Gas boiler installations cost upwards of £2,000, but you can get them much cheaper elsewhere —Sunday Times, 2007.

3. The adverb upwardly occurs mainly in the expression upwardly mobile, meaning ‘aspiring to social and professional advancement’.

Modern English usage. 2014.