概算 and 計算: an estimated cost and the act of calculation
Compare roughly estimating material costs with carrying out a calculation, without treating calculation alone as proof of an accurate final amount.
A rough calculation before details are final
概算, read がいさん, means a rough calculation. 見積書を作る前に、必要な材料費を概算した。 says that necessary material costs were roughly calculated before making a quotation.
この金額は概算です。 identifies the amount as an estimate. Checking assumptions such as quantities and prices allows comparison with a later finalized amount.
The fact of carrying out a calculation
計算, read けいさん, means calculation. 買い物の合計金額を暗算で計算した。 says that the total shopping amount was calculated mentally.
計算の途中で符号を間違えた。 reports a sign error during calculation. The word 計算 itself does not guarantee an error-free answer.
Method and final status
概算も計算の一つです。 says that rough calculation is one kind of calculation. Do not contrast the two as calculating versus not calculating.
概算した金額を、実際の材料費と比べました。 says that the estimated amount was compared with actual material costs. The act of comparison does not establish equality.
Does 合計金額を計算しました。 establish an accurate final amount?
Show the answer and why
No. It reports calculating the total. Errors and whether costs are final require separate confirmation.