estimate

An estimate is a judgement of a size, value, amount, cost, etc., which is based on incomplete information.

Example: British Telecom will give you an estimate of the cost before doing any work.

If you estimate the number, size, value, amount, cost, etc. of something, you guess based on incomplete information.

Example: It's difficult to estimate how long it will take to get to London because we don't know how bad the traffic will be.