Fundamental constants
| 常量Constant | 符号Symbol | 数值Value |
|---|---|---|
| 真空光速Speed of light | c | 299 792 458 m/s |
| 普朗克常量Planck constant | h | 6.626 070 15 × 10⁻³⁴ J·s |
| 基本电荷Elementary charge | e | 1.602 176 634 × 10⁻¹⁹ C |
| 玻尔兹曼常量Boltzmann constant | k | 1.380 649 × 10⁻²³ J/K |
| 阿伏伽德罗常量Avogadro constant | NA | 6.022 140 76 × 10²³ /mol |
| 摩尔气体常量Molar gas constant | R | 8.314 462 618 J/(mol·K) |
| 标准重力加速度Standard gravity | g | 9.806 65 m/s² |
| 标准大气压Standard atmosphere | atm | 101 325 Pa |
The first six values above are exact by definition after the 2019 revision of the SI, so they carry no uncertainty and their digit count is a convention; g = 9.80665 m/s², by contrast, is an agreed standard value while actual local gravity varies slightly (about 9.78 at the equator and 9.83 at the poles). For engineering work 9.8 is usually enough, 9.80665 suits more careful work, and higher precision means looking up local measurements.
Common material densities
| 材料Material | 密度Density | 备注Note |
|---|---|---|
| 水（4℃）Water (4 °C) | 1000 | 1 立方米约 1 吨1 m³ ≈ 1 tonne |
| 冰Ice | 917 | 比水轻，故浮于水面Lighter than water, so it floats |
| 酒精（乙醇）Ethanol | 789 | 比水轻Lighter than water |
| 空气（标准状态）Air (standard) | 1.293 | 随温度气压变化Varies with T and p |
| 铝Aluminium | 2700 | 轻金属Light metal |
| 钢 / 铁Steel / iron | 7850 – 7870 | 常用 78507850 is typical |
| 铜Copper | 8960 | 导电导热好Good conductor |
| 混凝土Concrete | 2300 – 2500 | 配筋后更高Higher when reinforced |
Energy and power conversions
| 换算Conversion | 数值Value | 应用场景Used for |
|---|---|---|
| 1 cal → J | 4.184 J | 热量换算Heat |
| 1 kcal → kJ | 4.184 kJ | 食物热量标签Food labels |
| 1 kWh → MJ | 3.6 MJ | 电费计量Electricity billing |
| 1 公制马力 → W | 735.49875 W | 汽车功率（PS）Metric horsepower |
| 1 英制马力 → W | 745.699872 W | 英美标称（hp）Imperial horsepower |
| 1 in → cm | 2.54 cm | 屏幕与管径Screens and pipes |
| 1 lb → g | 453.59237 g | 重量换算Weight |
| 1 mi → km | 1.609344 km | 里程Distance |
需要连续换算时用 单位换算（长度/质量/能量/功率）或 单位换算练习，比手算更稳。For chained conversions use the unit converter (length, mass, energy, power) or the conversion drill.
How to read these numbers
First, check the source: defined values are exact, measured values carry uncertainty, and agreed values such as g or the standard atmosphere hold only under stated conditions. Second, check significant figures: a constant quoted to seven digits does not make your result seven digits accurate — the coarsest input decides. Third, watch the unit system: mixing watts with horsepower, calories with joules, or kilograms with pounds is a classic source of errors, so convert everything to SI before substituting. Fourth, check the conditions: density changes with temperature (water is densest near 4 °C) and pressure falls with altitude (about 90 kPa at 1,000 m), so state your assumptions for engineering approximations.
Everyday formulas
A few combinations are worth remembering: kinetic energy E = ½mv²; gravitational potential E = mgh (with g as 9.8 or 9.80665); heating water Q = m × c × ΔT, where the specific heat of water is about 4,200 J/(kg·K) — so raising 1 kg by 1 °C takes 4,200 joules, roughly one kilocalorie; power P = W / t, and one unit of electricity is 1 kWh; the ideal gas law pV = nRT gives about 24 litres per mole at room temperature and pressure. The arithmetic is easy; unit consistency is the hard part, and the unit converter handles it more reliably.
FAQ
Should g be 9.8 or 9.80665?
For school and everyday calculations 9.8 is plenty (about 0.07% off); use 9.80665 for engineering standards and anything that must be checked. Actual local values vary with latitude and altitude — look them up for precise work.
Why does water density need a temperature?
Water is densest at about 4 °C (1,000 kg/m³); it thins as it warms and drops to roughly 917 when it freezes. Everyday calculations can use 1,000, but precise ones should state the temperature.
How far apart are metric and imperial horsepower?
About 1.4%: 735.49875 W for metric and 745.699872 W for imperial. Car specs labelled PS use metric horsepower while hp is usually imperial, so check before comparing outputs.