The most common and most likely answer to this crossword clue is the 8 letter word MENTALLY
I've seen this crossword clue in The Times
M
E
N
T
A
L
L
Y
More clues leading to the result MENTALLY
- People add up without using pencil and paper?
- People correspond, but not on paper
- Geezers add up numbers using their minds
- Counters count without calculator?
- Chaps try, losing heart, to keep everything in mind
- People agree rationally
- People add up in their heads
- People correspond, but not physically
- People agree that’s how to do brain operations
- People add up in the head
Buddy explains!

The straight part
We know that "without calculator" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case without calculator = mentally.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does MENTALLY mean?
MENTALLY adverb- In a mental manner; an idea thought out in one's mind, as opposed to an idea spoken orally.