一、运动与力学
长度
$1\ \text{km} = 10^3\ \text{m}$
$1\ \text{cm} = 10^{-2}\ \text{m}$
$1\ \text{mm} = 10^{-3}\ \text{m}$
$1\ \mu\text{m} = 10^{-6}\ \text{m}$
$1\ \text{nm} = 10^{-9}\ \text{m}$
$1\ \text{光年} \approx 9.46 \times 10^{15}\ \text{m}$（天体物理常用）
$1\ \text{km} = 10^3\ \text{m}$
$1\ \text{cm} = 10^{-2}\ \text{m}$
$1\ \text{mm} = 10^{-3}\ \text{m}$
$1\ \mu\text{m} = 10^{-6}\ \text{m}$
$1\ \text{nm} = 10^{-9}\ \text{m}$
$1\ \text{光年} \approx 9.46 \times 10^{15}\ \text{m}$（天体物理常用）
体积 / 容积
$1\ \text{m}^3 = 10^3\ \text{L}$（升）
$1\ \text{L} = 1\ \text{dm}^3 = 10^{-3}\ \text{m}^3$
$1\ \text{mL} = 1\ \text{cm}^3 = 10^{-6}\ \text{m}^3$
$1\ \text{mm}^3 = 10^{-9}\ \text{m}^3$
$1\ \text{gal（美）} \approx 3.785\ \text{L}$（英制，拓展）
$1\ \text{m}^3 = 10^3\ \text{L}$（升）
$1\ \text{L} = 1\ \text{dm}^3 = 10^{-3}\ \text{m}^3$
$1\ \text{mL} = 1\ \text{cm}^3 = 10^{-6}\ \text{m}^3$
$1\ \text{mm}^3 = 10^{-9}\ \text{m}^3$
$1\ \text{gal（美）} \approx 3.785\ \text{L}$（英制，拓展）
时间
$1\ \text{h} = 60\ \text{min} = 3600\ \text{s}$
$1\ \text{ms} = 10^{-3}\ \text{s}$
$1\ \mu\text{s} = 10^{-6}\ \text{s}$
$1\ \text{ns} = 10^{-9}\ \text{s}$
$1\ \text{h} = 60\ \text{min} = 3600\ \text{s}$
$1\ \text{ms} = 10^{-3}\ \text{s}$
$1\ \mu\text{s} = 10^{-6}\ \text{s}$
$1\ \text{ns} = 10^{-9}\ \text{s}$
速度
$1\ \text{m/s} = 3.6\ \text{km/h}$
$1\ \text{km/h} = \frac{1}{3.6}\ \text{m/s} \approx 0.278\ \text{m/s}$
$1\ \text{马赫} \approx 340\ \text{m/s}$（标准大气压、15°C）
$1\ \text{m/s} = 3.6\ \text{km/h}$
$1\ \text{km/h} = \frac{1}{3.6}\ \text{m/s} \approx 0.278\ \text{m/s}$
$1\ \text{马赫} \approx 340\ \text{m/s}$（标准大气压、15°C）
加速度
$1\ \text{m/s}^2 = 100\ \text{cm/s}^2$
$1\ \text{cm/s}^2 = 10^{-2}\ \text{m/s}^2$
$1\ \text{m/s}^2 = 100\ \text{cm/s}^2$
$1\ \text{cm/s}^2 = 10^{-2}\ \text{m/s}^2$
质量
$1\ \text{t} = 10^3\ \text{kg}$
$1\ \text{g} = 10^{-3}\ \text{kg}$
$1\ \text{mg} = 10^{-6}\ \text{kg}$
$1\ \text{原子质量单位}\ u \approx 1.66054 \times 10^{-27}\ \text{kg}$
$1\ \text{t} = 10^3\ \text{kg}$
$1\ \text{g} = 10^{-3}\ \text{kg}$
$1\ \text{mg} = 10^{-6}\ \text{kg}$
$1\ \text{原子质量单位}\ u \approx 1.66054 \times 10^{-27}\ \text{kg}$
密度
$1\ \text{g/cm}^3 = 10^3\ \text{kg/m}^3$
$1\ \text{kg/m}^3 = 10^{-3}\ \text{g/cm}^3$
$1\ \text{g/mL} = 1\ \text{g/cm}^3$（水等常用）
$1\ \text{g/cm}^3 = 10^3\ \text{kg/m}^3$
$1\ \text{kg/m}^3 = 10^{-3}\ \text{g/cm}^3$
$1\ \text{g/mL} = 1\ \text{g/cm}^3$（水等常用）
力（牛顿）
$1\ \text{N} = 1\ \text{kg}\cdot\text{m}/\text{s}^2$
$1\ \text{达因} = 10^{-5}\ \text{N}$（CGS制）
$1\ \text{kgf} \approx 9.8\ \text{N}$（公斤力，工程常用）
$1\ \text{N} = 1\ \text{kg}\cdot\text{m}/\text{s}^2$
$1\ \text{达因} = 10^{-5}\ \text{N}$（CGS制）
$1\ \text{kgf} \approx 9.8\ \text{N}$（公斤力，工程常用）
功 / 能 / 热量
$1\ \text{J} = 1\ \text{N}\cdot\text{m} = 1\ \text{kg}\cdot\text{m}^2/\text{s}^2$
$1\ \text{cal} = 4.186\ \text{J}$（热功当量）
$1\ \text{kWh} = 3.6 \times 10^6\ \text{J}$（电能）
$1\ \text{eV} = 1.602 \times 10^{-19}\ \text{J}$（电子伏特）
$1\ \text{J} = 1\ \text{N}\cdot\text{m} = 1\ \text{kg}\cdot\text{m}^2/\text{s}^2$
$1\ \text{cal} = 4.186\ \text{J}$（热功当量）
$1\ \text{kWh} = 3.6 \times 10^6\ \text{J}$（电能）
$1\ \text{eV} = 1.602 \times 10^{-19}\ \text{J}$（电子伏特）
功率
$1\ \text{W} = 1\ \text{J/s}$
$1\ \text{kW} = 10^3\ \text{W}$
$1\ \text{马力} \approx 735\ \text{W}$
$1\ \text{W} = 1\ \text{J/s}$
$1\ \text{kW} = 10^3\ \text{W}$
$1\ \text{马力} \approx 735\ \text{W}$
压强
$1\ \text{Pa} = 1\ \text{N/m}^2$
$1\ \text{atm} = 1.013 \times 10^5\ \text{Pa} = 760\ \text{mmHg}$
$1\ \text{bar} = 10^5\ \text{Pa}$
$1\ \text{cmHg} \approx 1.333 \times 10^3\ \text{Pa}$
$1\ \text{Pa} = 1\ \text{N/m}^2$
$1\ \text{atm} = 1.013 \times 10^5\ \text{Pa} = 760\ \text{mmHg}$
$1\ \text{bar} = 10^5\ \text{Pa}$
$1\ \text{cmHg} \approx 1.333 \times 10^3\ \text{Pa}$
二、电磁学
电荷量
$1\ \text{C} = 1\ \text{A}\cdot\text{s}$
$1\ e = 1.602 \times 10^{-19}\ \text{C}$（元电荷）
$1\ \text{C} = 1\ \text{A}\cdot\text{s}$
$1\ e = 1.602 \times 10^{-19}\ \text{C}$（元电荷）
电流
$1\ \text{A} = 1\ \text{C/s}$
$1\ \text{mA} = 10^{-3}\ \text{A}$
$1\ \mu\text{A} = 10^{-6}\ \text{A}$
$1\ \text{A} = 1\ \text{C/s}$
$1\ \text{mA} = 10^{-3}\ \text{A}$
$1\ \mu\text{A} = 10^{-6}\ \text{A}$
电压 / 电动势
$1\ \text{V} = 1\ \text{J/C} = 1\ \text{W/A}$
$1\ \text{kV} = 10^3\ \text{V}$
$1\ \text{mV} = 10^{-3}\ \text{V}$
$1\ \text{V} = 1\ \text{J/C} = 1\ \text{W/A}$
$1\ \text{kV} = 10^3\ \text{V}$
$1\ \text{mV} = 10^{-3}\ \text{V}$
电阻
$1\ \Omega = 1\ \text{V/A}$
$1\ \text{k}\Omega = 10^3\ \Omega$
$1\ \text{M}\Omega = 10^6\ \Omega$
$1\ \Omega = 1\ \text{V/A}$
$1\ \text{k}\Omega = 10^3\ \Omega$
$1\ \text{M}\Omega = 10^6\ \Omega$
电功率
$P = UI$，单位：$1\ \text{W} = 1\ \text{V}\cdot\text{A}$
$P = UI$，单位：$1\ \text{W} = 1\ \text{V}\cdot\text{A}$
电容
$1\ \text{F} = 1\ \text{C/V}$
$1\ \mu\text{F} = 10^{-6}\ \text{F}$
$1\ \text{pF} = 10^{-12}\ \text{F}$
$1\ \text{F} = 1\ \text{C/V}$
$1\ \mu\text{F} = 10^{-6}\ \text{F}$
$1\ \text{pF} = 10^{-12}\ \text{F}$
磁感应强度 (特斯拉)
$1\ \text{T} = 1\ \text{Wb/m}^2 = 1\ \text{N/(A}\cdot\text{m)}$
$1\ \text{G} = 10^{-4}\ \text{T}$（高斯，CGS制）
$1\ \text{T} = 1\ \text{Wb/m}^2 = 1\ \text{N/(A}\cdot\text{m)}$
$1\ \text{G} = 10^{-4}\ \text{T}$（高斯，CGS制）
磁通量
$1\ \text{Wb} = 1\ \text{V}\cdot\text{s} = 1\ \text{T}\cdot\text{m}^2$
$1\ \text{Mx} = 10^{-8}\ \text{Wb}$（麦克斯韦）
$1\ \text{Wb} = 1\ \text{V}\cdot\text{s} = 1\ \text{T}\cdot\text{m}^2$
$1\ \text{Mx} = 10^{-8}\ \text{Wb}$（麦克斯韦）
电感
$1\ \text{H} = 1\ \text{V}\cdot\text{s/A}$
$1\ \text{mH} = 10^{-3}\ \text{H}$
$1\ \mu\text{H} = 10^{-6}\ \text{H}$
$1\ \text{H} = 1\ \text{V}\cdot\text{s/A}$
$1\ \text{mH} = 10^{-3}\ \text{H}$
$1\ \mu\text{H} = 10^{-6}\ \text{H}$
三、光学
频率 / 波长
$c = \lambda \nu$，真空中光速 $c = 3.00 \times 10^8\ \text{m/s}$
$1\ \text{nm} = 10^{-9}\ \text{m}$（常用于可见光：380~780 nm）
$1\ \text{Å} = 10^{-10}\ \text{m} = 0.1\ \text{nm}$（埃）
$c = \lambda \nu$，真空中光速 $c = 3.00 \times 10^8\ \text{m/s}$
$1\ \text{nm} = 10^{-9}\ \text{m}$（常用于可见光：380~780 nm）
$1\ \text{Å} = 10^{-10}\ \text{m} = 0.1\ \text{nm}$（埃）
光速
$c \approx 3.0 \times 10^8\ \text{m/s} = 3.0 \times 10^{10}\ \text{cm/s}$
$c \approx 3.0 \times 10^8\ \text{m/s} = 3.0 \times 10^{10}\ \text{cm/s}$
光度 / 照度（高中较少涉及）
$1\ \text{lm} = 1\ \text{cd}\cdot\text{sr}$（流明）
$1\ \text{lx} = 1\ \text{lm/m}^2$（勒克斯）
$1\ \text{lm} = 1\ \text{cd}\cdot\text{sr}$（流明）
$1\ \text{lx} = 1\ \text{lm/m}^2$（勒克斯）
四、热学
温度
$T(\text{K}) = t(^\circ\text{C}) + 273.15$
$\Delta T(\text{K}) = \Delta t(^\circ\text{C})$（温差数值相等）
$t(^\circ\text{F}) = \frac{9}{5}t(^\circ\text{C}) + 32$（华氏度）
$T(\text{K}) = t(^\circ\text{C}) + 273.15$
$\Delta T(\text{K}) = \Delta t(^\circ\text{C})$（温差数值相等）
$t(^\circ\text{F}) = \frac{9}{5}t(^\circ\text{C}) + 32$（华氏度）
摩尔气体常数
$R = 8.314\ \text{J/(mol}\cdot\text{K)} = 0.08206\ \text{L}\cdot\text{atm/(mol}\cdot\text{K)}$
（$1\ \text{L}\cdot\text{atm} \approx 101.325\ \text{J}$）
$R = 8.314\ \text{J/(mol}\cdot\text{K)} = 0.08206\ \text{L}\cdot\text{atm/(mol}\cdot\text{K)}$
（$1\ \text{L}\cdot\text{atm} \approx 101.325\ \text{J}$）
热导率 / 传热系数（扩展）
$1\ \text{W/(m}\cdot\text{K)} = 1\ \text{J/(s}\cdot\text{m}\cdot\text{K)}$
$1\ \text{W/(m}\cdot\text{K)} = 1\ \text{J/(s}\cdot\text{m}\cdot\text{K)}$
五、原子物理
能量（电子伏特）
$1\ \text{eV} = 1.602 \times 10^{-19}\ \text{J}$
$1\ \text{MeV} = 10^6\ \text{eV} = 1.602 \times 10^{-13}\ \text{J}$
$1\ \text{GeV} = 10^9\ \text{eV}$
$1\ \text{eV} = 1.602 \times 10^{-19}\ \text{J}$
$1\ \text{MeV} = 10^6\ \text{eV} = 1.602 \times 10^{-13}\ \text{J}$
$1\ \text{GeV} = 10^9\ \text{eV}$
质量亏损 / 原子质量
$1\ u = 1.66054 \times 10^{-27}\ \text{kg}$
$1\ u\cdot c^2 \approx 931.5\ \text{MeV}$（质能方程）
$1\ u = 1.66054 \times 10^{-27}\ \text{kg}$
$1\ u\cdot c^2 \approx 931.5\ \text{MeV}$（质能方程）
普朗克常数
$h = 6.626 \times 10^{-34}\ \text{J}\cdot\text{s} = 4.136 \times 10^{-15}\ \text{eV}\cdot\text{s}$
$h = 6.626 \times 10^{-34}\ \text{J}\cdot\text{s} = 4.136 \times 10^{-15}\ \text{eV}\cdot\text{s}$
玻尔半径
$a_0 = 5.2918 \times 10^{-11}\ \text{m} \approx 0.529\ \text{Å}$
$a_0 = 5.2918 \times 10^{-11}\ \text{m} \approx 0.529\ \text{Å}$
放射性活度
$1\ \text{Bq} = 1\ \text{衰变/s}$
$1\ \text{Ci} = 3.7 \times 10^{10}\ \text{Bq}$（居里）
$1\ \text{Bq} = 1\ \text{衰变/s}$
$1\ \text{Ci} = 3.7 \times 10^{10}\ \text{Bq}$（居里）
半衰期
单位：$\text{s}$、$\text{min}$、$\text{h}$、$\text{d}$、$\text{a}$（年）
$1\ \text{a} \approx 3.156 \times 10^7\ \text{s}$
单位：$\text{s}$、$\text{min}$、$\text{h}$、$\text{d}$、$\text{a}$（年）
$1\ \text{a} \approx 3.156 \times 10^7\ \text{s}$