Understanding Units: Metric, Imperial, and the Trouble In Between

单位详解：公制、英制和两者之间的麻烦

A unit of measurement is a contract. It is a shared agreement that "one metre is the distance light travels in 1/299,792,458 of a second", or "one foot is exactly 0.3048 metres", or "one cubit is the length of the forearm of whoever is standing closest". As long as both parties use the same contract, the number that comes out of the calculation is meaningful. The moment two systems meet and nobody checks, the result can range from mildly wrong to spectacularly catastrophic — and the gap between "metric" and "imperial" is full of such moments.

计量单位是一种契约。它是"一米等于光在 1/299,792,458 秒内走过的距离"或"一英尺精确等于 0.3048 米"或"一腕尺等于最近那个人的前臂长度"这样的共同约定。只要双方使用同一份契约，得出的数字就有意义。而一旦两个系统相遇、又没人核对，结果可能从轻微偏差到灾难性失败 —— 公制与英制之间的鸿沟里，就充满了这种故事。

The metric system: built to be simple

公制：天生简洁

The metric system emerged from the French Revolution in 1799, born of two ideas. First, units should be based on something physical and reproducible — initially a fraction of the Earth's meridian, later (in 1983) the speed of light. Second, the system should be decimal: every unit relates to the next by a factor of ten. One kilometre is 1,000 metres, one metre is 100 centimetres, one centimetre is 10 millimetres. There are no awkward twelves, sixteens, or fourteens.

公制诞生于 1799 年的法国大革命，源于两个理念：第一，单位应基于可复现的物理量 —— 最初是地球子午线的一段弧长，1983 年起改为光速；第二，整个体系应采用十进制：每相邻单位之间相差 10 倍。1 千米 = 1,000 米，1 米 = 100 厘米，1 厘米 = 10 毫米。没有别扭的 12、16 或 14。

That second idea is what makes metric so easy to teach and so hard to give up once you've learned it. A child who knows the decimal shift can convert any metric unit by moving a decimal point. The same child, faced with 12 inches in a foot, 3 feet in a yard, 5,280 feet in a mile, 8 fluid ounces in a cup, 16 cups in a gallon, and 14 pounds in a stone, has to memorize a different rule for every conversion.

第二个理念正是公制易于教学、一旦学会就难以割舍的原因。懂十进制的小孩，转换任何公制单位只需移动小数点。而同样的小孩，遇到 1 英尺 = 12 英寸、1 码 = 3 英尺、1 英里 = 5,280 英尺、1 杯 = 8 液量盎司、1 加仑 = 16 杯、1 英石 = 14 磅时，必须为每一种换算单独记忆。

In 1875, the Treaty of the Metre established an international bureau (now the Bureau International des Poids et Mesures, BIPM, near Paris) to maintain the standards. Today, every country in the world has adopted the metric system as either its primary or its only official system of measurement, with one stubborn holdout for everyday use.

1875 年，《米制公约》设立了国际计量局（即今天的国际度量衡局 BIPM，位于巴黎附近）来维护度量衡标准。今天，全球所有国家都已在日常或官方层面采纳公制，只有一个国家在民用领域迟迟不切换。

The imperial mess: a pile of legacy constants

英制：堆叠的"历史常量"

"Imperial" is a polite name for what is really a museum of medieval and early-modern English weights and measures. The inch was once three barleycorns laid end to end. The foot was — the foot of a man. The pound has cycled through dozens of definitions over the centuries, each time when a new monarch decided the old coins were too light or too heavy. The US customary system is a fork of the British imperial system, frozen in time at the early 1800s, which is why a US gallon is roughly five-sixths of a UK gallon, and a US ton is the short ton while the UK uses the long ton.

"英制"其实只是对"中世纪和近代英国度量衡博物馆"的礼貌说法。1 英寸曾经等于 3 颗大麦粒首尾相接；1 英尺就是字面意义上的"一只脚"；1 磅在几个世纪里换过几十种定义，每次都是因为新国王觉得旧硬币太轻或太重。美制单位是英制在 19 世纪初的"分叉版本"，因此 US 加仑大约是 UK 加仑的六分之五；US 吨是"短吨"，而英国用的是"长吨"。

Some of the more memorable numbers in US customary units:

美制单位里一些令人难忘的数字：

• 12 inches in a foot, 3 feet in a yard, 1,760 yards (5,280 feet) in a mile.
• 1 英尺 = 12 英寸，1 码 = 3 英尺，1 英里 = 1,760 码 = 5,280 英尺。
• 16 dry ounces in a pound, but 16 fluid ounces in a pint only by a different definition.
• 1 磅 = 16 盎司（干量），而 1 品脱的液量盎司用的是另一个 16。
• 14 pounds in a stone (UK), 2,000 pounds in a US short ton, 2,240 pounds in a UK long ton.
• 1 英石 = 14 磅（英国），1 美制短吨 = 2,000 磅，1 英制长吨 = 2,240 磅。
• A fluid ounce of water weighs about 1.04 ounces (avoirdupois) — not exactly one ounce, not exactly different.
• 1 液量盎司的水重约 1.04 常衡盎司 —— 既不是精确的 1 盎司，也不是精确的"不同"。

The result is a system whose units are easy to define ("this is what my grandfather called a foot") but extremely hard to convert, calculate, or teach. NASA has been using metric internally since 1990, but US road signs still say "miles", US recipes still say "cups", and US construction still calls 2×4 lumber "two by four" even though the actual dimensions are 1.5 × 3.5 inches.

结果是：这个系统的单位很容易定义（"我爷爷叫它一英尺那么长"），但换算、计算和教学都极其困难。NASA 自 1990 年起在内部全面使用公制，但美国路标仍写"英里"、菜谱仍写"杯"、建筑木材还叫"2×4"，尽管实际尺寸是 1.5 × 3.5 英寸。

Mars Climate Orbiter: a $327 million unit mistake

火星气候探测器：3.27 亿美元的单位错误

On 23 September 1999, NASA's Mars Climate Orbiter — a $327 million spacecraft — burned up in the Martian atmosphere because the navigation team at Lockheed Martin in Colorado was sending thruster firing commands in pound-force seconds, while the flight team at JPL in California was interpreting them in newton seconds. One is roughly 4.45 times larger than the other. Across the eleven-month cruise, that small ratio compounded into a 170 km altitude error at Mars. The spacecraft dipped too deep, broke apart, and the mission was lost.

1999 年 9 月 23 日，NASA 的火星气候探测器（造价 3.27 亿美元）在火星大气中烧毁。原因是：科罗拉多州洛克希德·马丁的导航团队以"磅力·秒"为单位发送推进器指令，而加州 JPL 的飞控团队将其解读为"牛顿·秒"。两者相差约 4.45 倍。在长达 11 个月的巡航过程中，这个比值不断累积，最终在到达火星时形成 170 公里的高度偏差。探测器一头扎进大气层、机身解体，任务失败。

The post-mortem report is short and brutal: the navigation software failed to convert units between two systems, and there was no independent end-to-end check that would have caught the discrepancy. In response, NASA made metric the official language of all future missions, mandated independent verification of any software that moves numbers between teams, and made "check the units" one of the most quoted aphorisms in engineering.

事故调查报告简短而残酷：导航软件没有在两套单位之间做转换，也没有任何端到端的独立校验来发现偏差。NASA 此后宣布公制为今后所有任务的官方语言，要求对任何跨团队传递数据的软件进行独立验证，并把"先检查单位"奉为工程界最常被引用的话之一。

The lesson generalizes. Anywhere two pieces of software, two spreadsheets, or two teams exchange numbers, an unstated unit assumption can sit in the middle of the data path and silently corrupt the result. In a 2018 report, NIST estimated that unit confusion in US industry costs somewhere in the low billions of dollars per year. The fix is not cleverer software — it is declaring units explicitly, at the boundary of every system, every time.

这个教训具有普适性。任何两段软件、两张电子表格、两支团队相互传递数据时，中间都可能藏着一个未声明的"单位假设"，悄悄把结果算错。NIST 在 2018 年的一份报告里估计，美国工业每年因单位混淆造成的损失在数十亿美元量级。解决办法不是更聪明的软件，而是在每个系统的边界、每一次传递都显式声明单位。

Why the United States never switched

为什么美国一直没有完成切换

The metric system has been legal in the United States since 1866, and "the metric system shall be the preferred system of weights and measures for United States trade and commerce" has been the law since the Metric Act of 1975. The country has no metric mandate for everyday use. Why?

公制自 1866 年起在美国就是合法单位，1975 年的《公制法案》更规定"公制应作为美国贸易和商业的优选度量衡"。但在日常使用层面，美国并没有强制规定。

• Cost. A full conversion would require re-labelling every road sign, re-tooling every factory, re-writing every textbook and law, and re-training every tradesperson. The price tag has been estimated at anywhere from $10 billion to over $300 billion depending on the scope.
• 成本。 完全切换意味着重写所有路牌、改造所有工厂、重写所有教材法律、再培训所有技术工人。估算从 100 亿到超过 3,000 亿美元不等，取决于范围。
• Cultural inertia. Generations of Americans have learned to think in pounds, feet, and gallons. "A pint's a pound the world around" is a comforting rhyme, even though it is only approximately true for water.
• 文化惯性。 一代又一代美国人习惯了用磅、英尺、加仑思考。"一磅一品脱全世界都一样"是个让人安心的顺口溜，尽管对水来说只是"近似"成立。
• The 1980s voluntary approach. The US Metric Board was defunded in 1982, leaving conversion to market forces. Some industries moved (soft drinks are now sold in 2-liter bottles, hard drives in gigabytes, pharmaceuticals in milligrams) while others did not (road distances, house lots, human height).
• 1980 年代的"自愿切换"路线。 美国公制委员会 1982 年被取消经费，把转换交给了市场。有些行业切换了（汽水用 2 升装、硬盘用 GB、药品用毫克），有些则没有（公路距离、地块、人体身高）。
• No crisis. Every other country that switched had a revolution, a war, or a national reconstruction. The US has not had an event severe enough to overcome the inertia, so it lives with two parallel systems in daily life.
• 没有危机推动。 其他成功切换的国家都经历过革命、战争或国家重建。美国一直没有这种量级的事件来打破惯性，因此生活中长期并存两套系统。

The practical effect is that American engineers, scientists, doctors, and pharmacists all routinely use metric, while American cooks, drivers, and homebuyers all routinely use imperial. The country has, in effect, achieved a soft transition in technical fields and a hard resistance everywhere else.

实际结果是：美国工程师、科学家、医生、药剂师日常都在用公制；美国厨师、司机、买房者则日常在用英制。这个国家事实上在技术领域完成了软切换，在其他所有领域则顽强坚守旧制。

Aviation: feet, nautical miles, and knots

航空：英尺、海里与节

Modern aviation is a fascinating fossil. The world is metric, and the planes are mostly built in countries that have officially adopted the metric system, but flight levels are still stated in feet, distances in nautical miles, and speeds in knots. The reason is mostly historical and operational.

现代航空是一个迷人的"活化石"。全世界都用公制，飞机的制造国大多官方采用公制，但飞行高度层仍用英尺、距离仍用海里、速度仍用节。原因是历史和操作层面的。

• A nautical mile is one minute of arc on the Earth's surface, which makes it easy to compute distance from a latitude/longitude grid. It is exactly 1,852 metres by international definition since 1929.
• 1 海里等于地球表面 1 分的弧长，因此从经纬度网格计算距离非常方便。1929 年起国际定义为精确的 1,852 米。
• A knot is one nautical mile per hour, so a speed in knots translates directly to a position change in minutes of latitude. Pilots read charts in nautical miles, and the math stays in one consistent unit.
• 1 节等于 1 海里/小时，因此以"节"表示的速度可以直接换算成"纬度分钟"的位置变化。飞行员以海里读图，整个运算保持单位一致。
• Altitude in feet is a US inheritance, kept by international agreement because changing it would require retraining every pilot and rewriting every procedure. A "flight level" is exactly 100 feet, so FL350 means 35,000 feet.
• 高度用英尺来自美国传统，根据国际协议被保留下来，因为改用其他单位意味着重新培训每位飞行员、重写每一条程序。"飞行高度层"恰好是 100 英尺，所以 FL350 就是 35,000 英尺。

The result is a global system that uses metric for everything internal (fuel in kilograms or litres, distances on the ground in kilometres) and pre-metric imperial for everything that goes through the cockpit instruments. The cockpit is one of the last strongholds of the foot, the nautical mile, and the knot.

结果是：一套全球系统，内部事务用公制（燃油用千克或升、地面距离用公里），而所有进入驾驶舱仪表的数据仍用前公制时代的英制。驾驶舱是英尺、海里和节最后的堡垒之一。

The case for sticking with one system

坚持使用单一系统的理由

Mixing measurement systems is not just a curiosity. It costs time, money, and occasionally lives. The case for a single system is straightforward:

混用度量衡系统不只是趣闻，它会消耗时间、金钱，偶尔还会付出生命。坚持单一系统的理由很简单：

• Decimal math is easier. 3.5 km × 2 = 7 km. Three and a half miles times two is "seven", but multiplying yards by feet by inches is a tour de force.
• 十进制计算更简单。 3.5 km × 2 = 7 km。3.5 英里乘以 2 仍要换算，而把码、英尺、英寸混在一起乘基本是杂技表演。
• Fewer conversions mean fewer errors. Every conversion is an opportunity to lose a factor of 2.54, 0.3048, 4.448, 0.454, or 1.609. Each is small, each is innocent, and together they have ended missions and damaged equipment.
• 换算越少，错误越少。 每次换算都可能丢掉一个 2.54、0.3048、4.448、0.454 或 1.609 的因子。每个都很小、看起来人畜无害，但合在一起已经终结过任务、损坏过设备。
• Standards are global. A bolt specified in millimetres fits a tool specified in millimetres in any country. A "3/8 inch" wrench works in California and does not work anywhere else, even though there is a perfectly good 9.5 mm wrench that does.
• 标准应当是全球的。 用毫米标称的螺栓，可以和任何国家里用毫米标称的工具配合。"3/8 英寸"的扳手在加州能用，到了别处就用不了，尽管其实有 9.5 毫米的扳手完全胜任。
• Children learn faster. The metric system can be taught to a seven-year-old in an afternoon. The imperial system can be taught to an engineering student in a semester.
• 孩子学得更快。 公制可以一个下午教给 7 岁的孩子。英制要花一学期才能教会工科大学生。

For everyday work, the rule is: pick one system and stay in it. If you must convert, write down the conversion factor next to the number, double-check it, and never let it live silently inside a chain of formulas. NIST publishes the official US definitions in Special Publication 811 ("Guide for the Use of the International System of Units"); it is short, free, and worth keeping open in a tab.

对日常工作来说，原则是：选定一个系统并坚持下去。如果一定要换算，把换算系数写在数字旁边，核对一遍，永远不要让它默默藏在一长串公式里。NIST 在特别出版物 SP 811（《国际单位制使用指南》）里给出了美国官方的定义；这份文档很短、免费，值得常驻标签页。

Try the tools

试试这些工具

Convert between metric and imperial units with the unit converter. It covers length, mass, temperature, area, and volume, and runs entirely in your browser.

用 单位转换器 在公制和英制之间互转。覆盖长度、质量、温度、面积和体积，所有计算都在浏览器中完成。