1. a straight line from the center to the circumference of a circle or sphere
半徑（從圓心或球心到圓周或球面的直線）
The radius of the circle is 5 centimeters.
這個圓的半徑是5公分。
To find the area, you need to know the radius.
要計算面積，你需要知道半徑。
Radius Meaning（定義、用法、例句與發音）
radius
noun
快速理解
What does "Radius" mean?What are 2-3 core uses of "Radius"?
「radius」主要指圓的半徑，也延伸指圓形區域或範圍。
- 1
幾何學：圓的半徑
EN: A straight line from the center to the circumference of a circle.
翻譯: 從圓心到圓周的一條直線。
- 2
圓形區域
EN: A circular area defined by a specific distance from a central point.
翻譯: 以某個中心點為基準，特定距離內的圓形區域。
- 3
範圍、影響圈
EN: The range or scope of activity, influence, or operation.
翻譯: 活動、影響力或運作的範圍。
- 4
解剖學：橈骨
EN: The shorter and thicker of the two bones in the human forearm.
翻譯: 人類前臂兩根骨頭中較短且較粗的那一根。
小提醒：注意複數形式是「radii」或「radiuses」。在非正式對話中，當指「範圍」時，常直接使用「within a 5-mile radius」這樣的說法，而不會特別強調其幾何學的根源。
發音（How to Pronounce "Radius" in English）
How to pronounce "Radius" in English?"Radius" US vs UK pronunciation
點擊下方的 US / UK 按鈕可播放發音。
Real-life Examples of "Radius" from YouTube Videos
Irwin Redlener: How to survive a nuclear attack
TED
“This is the ultimate, And if you're in the half-mile radius of where this bomb went off, you have a 90 percent chance of not making it.”
(1 out of 6)
Definitions（定義）
What are the definitions of "Radius"?How does "Radius" change by context?
2. a circular area measured by a given radius from a central point
半徑範圍（以某點為中心，特定半徑內的圓形區域）
The explosion could be heard within a radius of ten miles.
爆炸聲在十英里半徑範圍內都聽得到。
We searched for the lost dog in a two-kilometer radius around the park.
我們在公園周圍兩公里半徑的範圍內尋找走失的狗。
3. the thicker and shorter of the two bones in the human forearm
橈骨（人類前臂兩根骨頭中較粗短的那一根）
He fractured his radius in a skiing accident.
他在滑雪事故中摔斷了橈骨。
The radius and ulna work together to allow rotation of the wrist.
橈骨和尺骨協同工作，使手腕能夠旋轉。
Grammar & Patterns（句型）
What are common sentence patterns for "Radius"?How to make natural sentences with "Radius"?
| Pattern | Meaning | Example |
|---|---|---|
| radius + of + noun | 表示某物的半徑 | The radius of the Earth is about 6,371 kilometers. (地球的半徑約為6,371公里。) |
| within a + [measurement] + radius | 在特定距離的半徑範圍內 | The search covered an area within a 10-mile radius. (搜索範圍涵蓋了方圓10英里內的區域。) |
| a radius of + [measurement] | 一個...長度的半徑 | The explosion created a crater with a radius of fifty meters. (爆炸造成了一個半徑五十公尺的坑洞。) |
| the radius of + [circle/object] | 特定圓形或物體的半徑 | He calculated the radius of the circular garden. (他計算了那個圓形花園的半徑。) |
用法說明
How is "Radius" different from similar structures?What usage mistakes are common with "Radius"?
radius 的單複數形式
- radius 是單數名詞，指從圓心到圓周上任意一點的直線距離，或指這個距離所定義的圓形區域。
- radii 是源自拉丁語的標準複數形式，在數學、科學及正式書寫中最為常見。
- radiuses 是規則化的英語複數形式，雖然可以接受，但在技術性語境中較不常見。
- 當描述多個圓的「半徑」時，通常使用 radii；而 radiuses 有時會用於描述非技術性的、重複的放射狀結構（如輪輻）。
對比例句： EN: Calculate the radius of this circle. 翻譯: 計算這個圓的半徑。
EN:The radii of the three concentric circles are 2cm, 5cm, and 10cm.
翻譯:這三個同心圓的半徑分別是 2 公分、5 公分和 10 公分。
總結建議
在數學與正式寫作中，建議使用 radii 作為複數形式。
易混淆對比
What is the difference between "Radius" and similar words?How to choose "Radius" vs alternatives?
radius vs diameter
radius（半徑）是從圓心到圓周的直線距離，而 diameter（直徑）是穿過圓心、連接圓周上兩點的直線距離，直徑是半徑的兩倍長。
radius vs circumference
radius（半徑）是圓心到圓周的直線距離，而 circumference（圓周長）是整個圓形外圍的總長度。
radius vs area
radius（半徑）是圓心到圓周的直線距離，是一個長度單位；而 area（面積）是圓形平面所佔據的大小，是一個面積單位。
口語用法
How is "Radius" used in spoken English?What is the spoken vs formal difference for "Radius"?
引述
在對話中，當引述或提及一個特定的半徑數值或概念時，常會直接使用 "radius"。 EN: The engineer said the radius of the pipe needs to be exactly 5 centimeters. 翻譯: 工程師說管子的半徑必須剛好是5公分。
EN:So you're telling me the explosion affected everything within a 10-mile radius?
翻譯:所以你是說爆炸影響了方圓10英里內的所有東西？
語氣強調
為了強調範圍或距離的特定性，會在 "radius" 前加上形容詞或重讀。 EN: We searched the entire search radius twice and found nothing. 翻譯: 我們把整個搜索半徑範圍搜了兩遍，什麼也沒找到。
EN:That's a huge delivery radius for a small cafe.
翻譯:對一家小咖啡館來說，那真是個超大的外送半徑。
停頓填充
在思考或組織語句時，有時會用 "within a... radius" 這樣的結構作為填充，以爭取時間。 EN: The signal should be strong within a... let's say, 50-meter radius. 翻譯: 訊號在一個... 嗯，大概50公尺半徑內應該很強。
EN:Our service covers, uh, a five-kilometer radius from our store.
翻譯:我們的服務範圍涵蓋，呃，從我們店鋪算起五公里半徑內。
正式寫作注意：在學術、技術或正式文件中，"radius" 應精確使用，並避免口語中的停頓或模糊表述（如 "a huge radius"）。應使用具體數值與單位（例如："a radius of 15 km"），並確保其幾何或空間定義清晰無歧義。
常見短語
What common collocations use "Radius"?What fixed phrases with "Radius" should I remember?
within a radius of
within a radius of [distance]
在…半徑範圍內
radius around
a [distance] radius around [place/point]
圍繞…的…半徑範圍
blast radius
blast radius
爆炸半徑
action radius
action radius
行動半徑
radius of curvature
radius of curvature
曲率半徑
radius bone
radius (bone)
橈骨（前臂骨）
serving radius
serving radius
服務半徑
常見錯誤
What are common mistakes with "Radius"?Which "Radius" sentences look correct but are wrong?
×The radius of the circles are 5 cm.
✓The radius of the circles is 5 cm.
The subject is 'radius' (singular), not 'circles'. The verb must agree with the singular subject 'radius'.
×Draw a circle with a 10 cm radiuses.
✓Draw a circle with a 10 cm radius.
'Radius' is the singular form. The plural is 'radii' (Latin origin) or 'radiuses' (less common). Here, 'a' indicates singular, so 'radius' must be used.
×The explosion affected everything within radius of 5 kilometers.
✓The explosion affected everything within a radius of 5 kilometers.
The phrase 'a radius of [measurement]' requires the indefinite article 'a' before 'radius'.
×The school is located in a 2 km radius from the station.
✓The school is located within a 2 km radius of the station.
The correct prepositional phrase is 'within a [distance] radius of [a point]'. 'From' is incorrect in this context.
×If the radius is 8 m, the circle is 8 m across.
✓If the radius is 8 m, the circle is 16 m across.
The distance across a circle through its center is the 'diameter', which is twice the length of the radius (diameter = 2 × radius).
×We measured many radius and recorded them.
✓We measured many radii and recorded them.
'Radius' is a countable noun. When referring to more than one, the standard plural form is 'radii' (pronounced /ˈreɪ.di.aɪ/). 'Radiuses' is an accepted alternative but is less common.
詞形變化
What are the word forms of "Radius"?What are tense/participle forms of "Radius"?