---
id: css-math-functions
title: "CSS Math Functions"
category: "Frontend"
status: "draft"
verification_status: "conceptual"
canonical_id: ""
aliases: ["calc()", "min()", "max()", "clamp()", "CSS calc", "responsive sizing functions"]
duplicate_of: ""
source_trust_level: "B"
confidence_score: 0.9
created_at: 2026-06-23
updated_at: 2026-06-23
review_reason: ""
merge_history: []
tags: ["css", "web", "frontend", "w3schools", "math-functions", "calc", "responsive"]
raw_sources: ["https://www.w3schools.com/css/css_math_functions.asp"]
applied_in: []
github_commit: ""
---

# [[CSS Math Functions]]

## 🎯 한 줄 통찰 (One-line insight)
CSS math functions — `calc()`, `max()`, `min()`, and `clamp()` — let property values be computed (and mixed across units) at render time, enabling responsive sizing without JavaScript. [S1]

## 🧠 핵심 개념 (Core concepts)
- **`calc()`** — performs a mathematical calculation that will be used as the property value, supporting mixed units. [S1]
- **`max()`** — takes a comma-separated list of values and uses the largest value from the list as the property value. [S1]
- **`min()`** — takes a comma-separated list of values and uses the smallest value from the list as the property value. [S1]
- **`clamp()`** — sets a value that adjusts responsively between a minimum, a preferred, and a maximum value depending on the size of the viewport. [S1]

## 🧩 추출된 패턴 (Extracted patterns)
- **Mixed-unit arithmetic** — `calc()` combines incompatible units such as `%`, `px`, and `vh` in one expression (e.g. `calc(100% - 100px)`). [S1]
- **Responsive clamp pattern** — `clamp(min, preferred, max)` with a viewport-relative preferred value (e.g. `clamp(1.5rem, 5vw, 3rem)`) produces fluid typography and widths bounded at both ends. [S1]

## 📖 세부 내용 (Details)
**`calc()` — perform a calculation.** The `calc()` function performs a mathematical calculation that will be used as the property value. It supports addition, subtraction, multiplication, and division with mixed units. [S1]
```css
#div1 {
  margin: auto;
  width: calc(100% - 100px);
  height: calc(30vh + 50px);
  border: 1px solid black;
  padding: 10px;
}
```

**`max()` — use the largest value.** The `max()` function takes a comma-separated list of values, and uses the largest value from the list as the property value. [S1]
```css
#div1 {
  height: 100px;
  width: max(50%, 300px);
  border: 1px solid black;
  padding: 10px;
}
```

**`min()` — use the smallest value.** The `min()` function takes a comma-separated list of values, and uses the smallest value from the list as the property value. [S1]
```css
#div1 {
  height: 100px;
  width: min(50%, 300px);
  border: 1px solid black;
  padding: 10px;
}
```

**`clamp()` — responsive bounded value.** The `clamp()` function is used to set a value that will adjust responsively between a minimum value, a preferred value, and a maximum value depending on the size of the viewport. [S1]
```css
h2 {
  font-size: clamp(1.5rem, 5vw, 3rem);
}

div {
  border: 1px solid green;
  padding: 10px;
  font-size: clamp(1rem, 2.5vw, 2rem);
  width: clamp(200px, 50%, 600px);
}
```

## 🛠️ 적용 사례 (Applied in summary)
The page's applied demonstrations style a `#div1` box (and a `clamp()`-based heading/div pair) to show each function computing a live property value — for example a width that is the viewport minus 100px, or a font-size that scales with `5vw` but never below `1.5rem` or above `3rem`. No external project/commit applications found in the source.

## 💻 코드 패턴 (Code patterns)
Mixed-unit calculation (language: CSS):
```css
width: calc(100% - 100px);
height: calc(30vh + 50px);
```
Clamp for fluid, bounded sizing (language: CSS):
```css
font-size: clamp(1.5rem, 5vw, 3rem);
width: clamp(200px, 50%, 600px);
```

## ⚖️ 비교 및 선택 기준 (Comparison & decision criteria)
- **`calc()`** — when you need an exact arithmetic expression mixing units (e.g. fill the viewport minus a fixed sidebar). [S1]
- **`max()`** — when you want a floor: never smaller than the largest of the listed values. [S1]
- **`min()`** — when you want a ceiling: never larger than the smallest of the listed values. [S1]
- **`clamp()`** — when you want both a floor and a ceiling around a fluid preferred value in one declaration. [S1]

## ⚖️ 모순 및 업데이트 (Contradictions & updates)
No contradictions found in the source. (Note: the source page spells "preferred" as "preffered" in its `clamp()` description; corrected here.) [S1]

## ✅ 검증 상태 및 신뢰도
- **상태:** draft
- **검증 단계:** conceptual (실제 적용 사례 발견 시 applied/validated로 승격 가능)
- **출처 신뢰도:** B (W3Schools — widely used educational reference, not a primary standards body)
- **신뢰 점수:** 0.9
- **중복 검사 결과:** 신규 생성 (New discovery)

## 🔗 지식 그래프 (Knowledge Graph)
- **상위/루트:** [[CSS Tutorial]]
- **관련 개념:** [[CSS Units]], [[CSS Website Layout]], [[CSS Optimization]]
- **참조 맥락:** Used whenever a property value must be computed or made responsive across viewport sizes without scripting.

## 📚 출처 (Sources)
- [S1] W3Schools — CSS Math Functions — https://www.w3schools.com/css/css_math_functions.asp

## 📝 변경 이력 (Change history)
- 2026-06-23: Initial draft synthesized from the W3Schools "CSS Math Functions" page (Astra wiki-curation, P-Reinforce v3.1 format).