「calculus」主要有兩個核心含義：一是高等數學中的微積分學，二是醫學上指結石。
數學分支
EN: the branch of mathematics that deals with derivatives and integrals
翻譯: 微積分學，處理導數和積分的數學分支。
結石
EN: a hard mass that forms in the body, such as in the kidneys or on teeth
翻譯: 結石，在體內（如腎臟）或牙齒上形成的硬塊。
計算方法
EN: a particular method or system of calculation or reasoning
翻譯: 一種特定的計算或推理方法或體系。
小提醒：在數學語境外提到「calculus」時，常指醫學上的「結石」，例如「renal calculus」是腎結石，不要誤解為數學。
點擊下方的 US / UK 按鈕可播放發音。
Real-life Examples of "Calculus" from YouTube Videos
Christina Warinner: Tracking ancient diseases using ... plaque
TED
“It's a type of fossilized dental plaque that is called officially dental calculus. Many of you may know it by the term tartar.”
1. a branch of mathematics that deals with rates of change and the accumulation of quantities
微積分（數學的一個分支，研究變化率和量的累積）
Differential calculus is used to find the rate at which a quantity changes.
微分學用於找出一個量變化的速率。
She took a course in calculus during her first year of university.
她在大學一年級時修了一門微積分課程。
2. a particular method or system of calculation or reasoning
演算法；計算體系；推理方法
The moral calculus behind his decision was complex and controversial.
他決策背後的道德考量既複雜又具爭議性。
In game theory, players use a strategic calculus to predict opponents' moves.
在博弈論中，玩家使用策略演算法來預測對手的行動。
3. a hard mass formed in the body, especially on teeth or in the kidney
結石（體內形成的硬塊，尤指牙結石或腎結石）
Dental calculus, also known as tartar, can lead to gum disease if not removed.
牙結石，也稱為牙垢，如果不清除可能導致牙齦疾病。
The patient was diagnosed with renal calculus, requiring medical intervention.
該患者被診斷出患有腎結石，需要醫療介入。
| Pattern | Meaning | Example |
|---|---|---|
| calculus of + noun | ...的計算/演算 | The calculus of probabilities is essential for this model. (機率演算對這個模型至關重要。) |
| do/study + calculus | 學習微積分 | She decided to study calculus in her first year of university. (她決定在大一學習微積分。) |
| apply + calculus to + noun | 將微積分應用於... | Engineers apply calculus to solve complex design problems. (工程師應用微積分來解決複雜的設計問題。) |
| a problem in + calculus | 微積分中的一個問題 | This is a classic problem in calculus. (這是微積分中的一個經典問題。) |
| the fundamentals/basics of calculus | 微積分的基礎 | He has a solid grasp of the fundamentals of calculus. (他對微積分的基礎有扎實的掌握。) |
EN:A quick calculation showed the project was over budget.
翻譯:快速計算顯示該項目已超出預算。
EN:He studied differential calculus in university.
翻譯:他在大學學習了微分學。
EN:The calculation of the rocket's trajectory took hours.
翻譯:計算火箭的軌跡花了數小時。
當指涉數學系統或抽象的決策框架時使用 calculus，而指具體的運算行為或結果時則使用 calculation。
calculus vs algebra
「calculus」專注於變化率與累積量，如微分與積分；「algebra」則處理符號、方程式與抽象結構的運算。
calculus vs arithmetic
「calculus」是高階數學分支，涉及極限與連續性；「arithmetic」是基礎數學，處理數字的加減乘除。
calculus vs statistics
「calculus」是確定性的數學分析工具；「statistics」是處理數據收集、分析與機率的學科。
在對話中，當引述或提及他人對這個概念的說法時，會使用引述格式。 EN: He was like, "I can't wrap my head around this calculus problem." 翻譯: 他當時說：「我完全搞不懂這道微積分題目。」
EN:My friend keeps saying, "Calculus is the language of the universe."
翻譯:我朋友老是說：「微積分是宇宙的語言。」
在口語中，會透過重複或特定詞彙來強調對這個科目的感受或重要性。 EN: I have to study calculus, calculus, and more calculus this weekend. 翻譯: 我這個週末得一直讀微積分、微積分、還是微積分。
EN:That calculus exam was seriously brutal.
翻譯:那次微積分考試真的超級難。
在思考或組織語句時，可能會將此詞作為停頓點的一部分。 EN: So, the next topic is... calculus, I think? 翻譯: 所以，下一個主題是... 微積分，對吧？
EN:I'm struggling with, you know, calculus and physics.
翻譯:我在，你知道的，微積分和物理這兩科上很吃力。
正式寫作注意：在學術論文、正式報告或專業郵件中，應避免上述口語用法。請直接、明確地使用「calculus」（微積分）一詞，並搭配完整的學術性句子結構，例如 "The principles of calculus are applied to model the system's behavior."（微積分的原理被應用於模擬該系統的行為）。
differential calculus
noun
微分學
integral calculus
noun
積分學
lambda calculus
noun
λ演算
do the calculus
verb phrase
進行計算；權衡利弊
political calculus
noun
政治算計
renal calculus
noun
腎結石
master calculus
verb phrase
精通微積分
calculus of variations
noun
變分法
×I need to learn calculus for my biology class.
✓I need to learn calculus for my mathematics/physics/engineering class.
Calculus is a branch of mathematics primarily used in fields like physics, engineering, economics, and computer science, not typically a core requirement for basic biology studies. Using it with biology can sound unnatural unless referring to very specific advanced applications (e.g., mathematical biology).
×I have a calculus tomorrow.
✓I have a calculus exam/test/class tomorrow.
"Calculus" is an uncountable noun referring to the mathematical subject itself. You cannot have "a calculus" in the sense of an event or item. You must specify what related to calculus (e.g., an exam, a book, a lesson) you are referring to.
×I am good at calculus.
✓I am good at calculus. / I do well in calculus.
While this sentence is grammatically correct, learners often use it incorrectly by confusing "calculus" with "calculation" or basic arithmetic. The mistake is conceptual: claiming to be good at calculus implies proficiency in advanced topics like derivatives and integrals, not just simple math. The correction is the same sentence, but the note highlights the potential semantic confusion.
×We learned about kidney calculus in math class.
✓We learned about kidney stones in biology/medical class. / We learned about (infinitesimal) calculus in math class.
"Calculus" in a medical context means a stone (e.g., kidney calculus, dental calculus/tartar). In an academic context, it almost always refers to the mathematical system. Using the medical term in a math context is incorrect and confusing. The mathematical subject is fully named "infinitesimal calculus," often shortened to just "calculus."
×I need to buy a new calculus.
✓I need to buy a new calculus textbook.
Similar to mistake #2, "calculus" is uncountable. You cannot buy "a calculus." You must specify the countable item related to calculus, such as a textbook, calculator, or software.
×The calculus of the situation was complex.
✓The calculation/analysis of the situation was complex.
While "calculus" can metaphorically mean a system or method of analysis (e.g., "political calculus"), this is an advanced, figurative use. Learners often mistakenly use "calculus" as a fancy synonym for "calculation" or "computation." In most everyday contexts about figuring something out, "calculation" or "analysis" is more natural and accurate.