📚 IB and CCEA Science: Formula Summary Handbook | IB与CCEA科学公式汇总手册
This handbook brings together the essential formulas required for IB Diploma science subjects (Biology, Chemistry, Physics) and their direct counterparts in CCEA GCE specifications, providing a bilingual quick-reference tool for students who study across these curricula. Understanding and memorising these relationships is fundamental for solving numerical problems, designing experiments, and interpreting scientific data in examinations.
本手册汇集了IB文凭课程科学科目（生物、化学、物理）以及CCEA GCE考试大纲中直接对应的核心公式，为跨课程学习的学生提供一份中英双语速查工具。理解并记住这些关系，对于解决计算题、设计实验和解读考试中的科学数据至关重要。
1. Kinematics | 运动学
Kinematic equations describe motion with uniform acceleration. They link displacement, velocity, acceleration, and time, forming the backbone of mechanics problem-solving.
运动学方程描述匀加速运动，它们将位移、速度、加速度和时间联系起来，是解决力学问题的基石。
v = u + at
This is the first SUVAT equation. v represents final velocity (m/s), u initial velocity (m/s), a constant acceleration (m/s²), and t time taken (s). It is used when acceleration is constant and displacement is not required.
这是第一个SUVAT方程。v代表末速度（m/s），u为初速度（m/s），a为恒定加速度（m/s²），t为时间（s）。当加速度恒定且不需要位移时使用。
s = ut + ½at²
This equation calculates displacement s (m) for uniformly accelerated motion from an initial velocity u. It is particularly useful when the final velocity is unknown.
该公式用于从初速度u开始计算匀加速运动的位移s（m）。在末速度未知时特别有用。
v² = u² + 2as
This relationship eliminates time t, connecting initial and final velocities directly to acceleration and displacement. Essential for problems where time is not given.
该关系式消去了时间t，将初、末速度直接与加速度和位移关联。对于未给出时间的问题至关重要。
2. Forces and Dynamics | 力与动力学
Newton’s laws provide quantitative descriptions of forces and motion. The formulas here allow calculation of resultant force, weight, and momentum changes.
牛顿定律给出了力与运动的定量描述。以下公式可计算合外力、重量和动量变化。
F = ma
Newton’s second law: the resultant force F (N) acting on an object is equal to its mass m (kg) multiplied by its acceleration a (m/s²). Direction of acceleration matches the net force.
牛顿第二定律：作用在物体上的合外力F（N）等于其质量m（kg）乘以加速度a（m/s²）。加速度方向与合外力方向一致。
W = mg
Weight W (N) is the force due to gravity, calculated as mass m (kg) times gravitational field strength g (N/kg). On Earth, g ≈ 9.81 N/kg.
重量W（N）是由重力产生的力，等于质量m（kg）乘重力场强度g（N/kg）。地球表面g ≈ 9.81 N/kg。
p = mv
Momentum p (kg m/s) is the product of mass and velocity. Momentum is a vector quantity conserved in all isolated systems, crucial for collision analysis.
动量p（kg m/s）是质量与速度的乘积。动量是矢量，在孤立系统中守恒，对碰撞分析至关重要。
3. Work, Energy and Power | 功、能与功率
Energy calculations unify many areas of physics and chemistry. These formulas quantify mechanical work, kinetic and potential energy, and the rate of energy transfer.
能量计算将物理和化学多个领域统一起来。以下公式量化了机械功、动能、势能以及能量转移速率。
W = Fd cosθ
Work done W (J) is the force F (N) along the direction of displacement d (m). The angle θ between force and displacement must be considered; when force is parallel, W = Fd.
做功W（J）等于力F（N）在位移方向上的分量乘以位移d（m）。需要考虑力与位移夹角θ；当力与位移平行时，W = Fd。
Eₖ = ½mv²
Kinetic energy Eₖ (J) depends on mass m (kg) and speed v (m/s). This formula is fundamental in collision, conservation of energy, and gas molecule kinetic theory.
动能Eₖ（J）取决于质量m（kg）和速率v（m/s）。该公式在碰撞、能量守恒和气体分子动理论中都很基本。
ΔEₚ = mgΔh
The change in gravitational potential energy ΔEₚ (J) near the Earth’s surface is mass m (kg) × g (N/kg) × change in height Δh (m).
地球表面附近重力势能的变化ΔEₚ（J）等于质量m（kg）× g（N/kg）× 高度变化Δh（m）。
P = ΔW/Δt = Fv
Power P (W) is the rate of work done or energy transferred. For an object moving at constant speed v under constant force F in the same direction, power equals Fv.
功率P（W）是做功或能量转移的速率。对于在恒力F作用下以恒定速度v同向运动的物体，功率等于Fv。
4. Thermal Physics | 热物理学
Thermal physics formulas relate temperature, heat, internal energy, and gas behaviour. They are vital for understanding thermodynamic processes and ideal gases.
热物理公式将温度、热量、内能和气体行为关联起来，对理解热力学过程和理想气体至关重要。
Q = mcΔθ
The heat Q (J) required to change the temperature of a substance depends on its mass m (kg), specific heat capacity c (J/kg·°C), and temperature change Δθ (°C).
改变物质温度所需的热量Q（J）取决于其质量m（kg）、比热容c（J/kg·°C）和温度变化Δθ（°C）。
Q = mL
During a change of state, the heat Q (J) absorbed or released equals mass m (kg) times the specific latent heat L (J/kg). No temperature change occurs during the state change.
在状态变化过程中，吸收或释放的热量Q（J）等于质量m（kg）乘比潜热L（J/kg）。状态变化期间温度不变。
pV = nRT
The ideal gas equation links pressure p (Pa), volume V (m³), amount of substance n (mol), the gas constant R (8.31 J/mol·K), and temperature T (K). Used to model real gases at low pressure.
理想气体状态方程将压强p（Pa）、体积V（m³）、物质的量n（mol）、气体常数R（8.31 J/mol·K）和温度T（K）联系起来，用于在低压下模拟真实气体。
5. Waves and Optics | 波与光学
Wave properties are described by speed, frequency, and wavelength. Optics formulas govern refraction, lenses, and image formation, which are tested in both IB and CCEA physics papers.
波的特性通过波速、频率和波长来描述。光学公式涵盖折射、透镜和成像，在IB和CCEA物理试卷中均有考察。
v = fλ
The wave speed v (m/s) equals the frequency f (Hz) multiplied by the wavelength λ (m). This applies to all wave types including sound, light, and water waves.
波速v（m/s）等于频率f（Hz）乘以波长λ（m）。该式适用于包括声波、光波和水波在内的所有波型。
n = c / v
The refractive index n of a medium is the ratio of the speed of light in a vacuum c (3.00×10⁸ m/s) to its speed v in that medium. It determines how much light bends.
介质的折射率n是光在真空中的速度c（3.00×10⁸ m/s）与光在该介质中的速度v之比。它决定了光弯曲的程度。
n₁ sinθ₁ = n₂ sinθ₂ (Snell’s law)
Snell’s law relates the angles of incidence θ₁ and refraction θ₂ to the refractive indices of the two media. It is essential for ray diagrams and critical angle calculations.
斯涅尔定律将入射角θ₁和折射角θ₂与两种介质的折射率联系起来。在进行光线图和临界角计算时必不可少。
1/f = 1/u + 1/v
The lens equation connects focal length f (m), object distance u (m), and image distance v (m). Sign conventions depend on real/virtual images. The formula applies to thin converging and diverging lenses.
透镜方程联立焦距f（m）、物距u（m）和像距v（m）。符号规则取决于实像或虚像。该公式适用于薄凸透镜和凹透镜。
6. Electricity and Magnetism | 电与磁
Electric circuit analysis relies on a small set of formulas linking voltage, current, resistance, charge, and power. Magnetism formulas quantify magnetic force and flux.
电路分析依赖于一组关联电压、电流、电阻、电荷和功率的少量公式。磁学公式则量化磁力和磁通量。
V = IR
Ohm’s law states that the potential difference V (V) across a conductor is directly proportional to the current I (A) flowing through it, with resistance R (Ω) as the constant.
欧姆定律表明，导体两端的电势差V（V）与流过导体的电流I（A）成正比，电阻R（Ω）为比例常数。
P = IV = I²R = V²/R
Electrical power P (W) can be expressed in three equivalent forms using current I, voltage V, and resistance R. These forms are handy for series and parallel circuit analysis.
电功率P（W）可以用电流I、电压V和电阻R表示为三种等效形式。这些形式便于分析串联和并联电路。
Q = It
The charge Q (C) transferred is the product of current I (A) and time t (s). This links microscopic electron flow to macroscopic circuit measurements.
转移的电荷Q（C）是电流I（A）与时间t（s）的乘积。它将微观电子流动与宏观电路测量联系起来。
F = BIl sinθ
The magnetic force F (N) on a current-carrying wire in a magnetic field depends on flux density B (T), current I (A), length of wire l (m) within the field, and the angle θ between the wire and field lines.
通电导线在磁场中所受的磁力F（N）取决于磁通量密度B（T）、电流I（A）、磁场中导线的长度l（m）以及导线与磁感线的夹角θ。
7. Chemical Quantities and Reactions | 化学计量与反应
Stoichiometry is the heart of quantitative chemistry. These formulas allow chemists to convert between mass, moles, particles, and concentration, and to calculate percentage yield and atom economy.
化学计量是定量化学的核心。这些公式使化学工作者能够在质量、摩尔、粒子数和浓度之间进行转换，并计算产率和原子经济性。
n = m / M
The number of moles n (mol) is found by dividing the mass m (g) of a substance by its molar mass M (g/mol). This is the gateway to all stoichiometric calculations.
物质的量n（mol）由物质的质量m（g）除以其摩尔质量M（g/mol）求得。这是所有化学计量计算的基础。
c = n / V
Concentration c (mol/dm³) equals the amount of solute n (mol) divided by the volume of solution V (dm³). In IB and CCEA, common units are mol dm⁻³.
浓度c（mol/dm³）等于溶质的物质的量n（mol）除以溶液的体积V（dm³）。在IB和CCEA中，常用单位为mol dm⁻³。
N = n × Nₐ
The total number of entities N (atoms, molecules, ions) is moles n multiplied by Avogadro’s constant Nₐ (6.02×10²³ mol⁻¹).
粒子总数N（原子、分子、离子）等于物质的量n乘以阿伏伽德罗常数Nₐ（6.02×10²³ mol⁻¹）。
% yield = (actual yield / theoretical yield) × 100%
Percentage yield compares the mass of product actually obtained to the maximum theoretical mass predicted by stoichiometry, providing an efficiency measure for a reaction.
产率百分比将实际获得的产品质量与化学计量预测的最大理论质量进行比较，是反应效率的量度。
Atom economy = (molar mass of desired product / total molar mass of reactants) × 100%
Atom economy evaluates how much of the reactant atoms end up in the useful product, guiding the design of greener synthetic pathways.
原子经济性衡量反应物原子有多少最终进入有用产物，指导设计更绿色的合成路线。
8. Acids, Bases and pH | 酸、碱与pH
Acid-base calculations centre on pH, pOH, and equilibrium constants. These formulas apply to strong acids/bases as well as weak acid dissociation.
酸碱计算围绕pH、pOH和平衡常数展开。这些公式适用于强酸/强碱以及弱酸的电离。
pH = –log₁₀[H⁺]
The pH of a solution is the negative logarithm (base 10) of the hydrogen ion concentration [H⁺] in mol dm⁻³. A change of one pH unit represents a tenfold change in [H⁺].
溶液的pH是氢离子浓度[H⁺]（mol dm⁻³）的以10为底的负对数。pH值每变化1个单位，[H⁺]变化10倍。
pOH = –log₁₀[OH⁻]
Analogous to pH, pOH describes hydroxide ion concentration. At 298 K, pH + pOH = 14 for aqueous solutions.
与pH类似，pOH描述氢氧根离子浓度。在298 K时，水溶液中pH + pOH = 14。
Kₐ = [H⁺][A⁻] / [HA]
The acid dissociation constant Kₐ quantifies the strength of a weak acid HA. The smaller the pKₐ (–log Kₐ), the stronger the acid.
酸解离常数Kₐ量化弱酸HA的强度。pKₐ（–log Kₐ）越小，酸性越强。
K_w = [H⁺][OH⁻] = 1.0×10⁻¹⁴ (at 298 K)
The ionic product of water K_w is constant at a given temperature. It links [H⁺] and [OH⁻] in all dilute aqueous solutions.
水的离子积K_w在给定温度下为常数。它将所有稀水溶液中的[H⁺]和[OH⁻]关联起来。
9. Redox and Electrochemistry | 氧化还原与电化学
Electrochemistry formulas connect measurable quantities like current, time, and cell potential to the amount of substance transformed in redox reactions.
电化学公式将电流、时间和电池电势等可测量量与氧化还原反应中转变的物质的量联系起来。
ΔG° = –nFE°
The standard Gibbs free energy change ΔG° (J) for a redox reaction is related to the number of electrons transferred n, Faraday constant F (96,500 C mol⁻¹), and standard cell potential E° (V). A negative ΔG° indicates a spontaneous reaction.
氧化还原反应的标准吉布斯自由能变ΔG°（J）与转移电子数n、法拉第常数F（96,500 C mol⁻¹）和标准电池电势E°（V）相关。ΔG°为负表明反应自发。
Q = n(e⁻) × F
The total charge Q (C) passed during electrolysis equals the moles of electrons n(e⁻) multiplied by Faraday’s constant. This directly links electric charge to chemical change.
电解过程中通过的总电荷Q（C）等于电子的物质的量n(e⁻)乘以法拉第常数。这直接将电荷与化学变化联系起来。
E°_cell = E°_cathode – E°_anode
The standard cell potential is calculated from standard reduction potentials of the two half-cells. It predicts the direction of electron flow and the feasibility of a redox reaction.
标准电池电势由两个半电池的标准还原电势计算得出。它可预测电子流动方向和氧化还原反应的可行性。
10. Biological Formulas | 生物公式
Quantitative skills in IB Biology and CCEA Life Sciences require handling magnification, size, rates, and statistical tests. These formulas frequently appear in data-based questions.
IB生物学及CCEA生命科学中的定量技能需要处理放大倍数、尺寸、速率和统计检验。这些公式经常出现在基于数据的问题中。
Magnification = Image size / Actual size
Magnification has no units; it is a ratio. When using a microscope, total magnification = eyepiece magnification × objective lens magnification.
放大率无单位，是一个比值。使用显微镜时，总放大倍数 = 目镜放大倍数 × 物镜放大倍数。
Heart rate (bpm) = 60 / time for one beat (s)
Heart rate in beats per minute is calculated from the interval between successive heartbeats. This is used in ECG data interpretation and exercise physiology.
以每分钟心跳次数为单位的心率，由连续心跳之间的间隔计算得出。该公式用于心电图数据解读和运动生理学。
Rate of reaction = Change in concentration / time
For enzyme-catalysed reactions, the rate can be expressed as decrease in substrate concentration or increase in product concentration per unit time.
对于酶催化反应，速率可表示为单位时间内底物浓度的减少量或产物浓度的增加量。
Surface area : volume ratio = SA / V
This ratio is fundamental to understanding diffusion, heat loss, and cell size limitations. As an object becomes larger, its SA:V ratio decreases.
该比值是理解扩散、热量散失和细胞大小限制的基础。随着物体变大，其表面积与体积之比下降。
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