IGCSE CIE Physics Formula Handbook | IGCSE CIE 物理公式汇总手册

📚 IGCSE CIE Physics Formula Handbook | IGCSE CIE 物理公式汇总手册

This ultimate formula handbook covers all essential equations for the IGCSE CIE Physics (0625) syllabus. Whether you are revising for mocks or your final examination, having these formulas at your fingertips will boost your confidence and save precious time. The formulas are grouped by topic, with clear variable definitions and common applications. Master the relationships, understand the units, and you will master the physics.

这份终极公式手册涵盖了 IGCSE CIE 物理 (0625) 教学大纲中所有关键的方程式。无论你是在准备模拟考试还是最终大考，将这些公式熟记于心都能提升你的信心并节省宝贵时间。公式按主题分组，配有清晰的变量定义和常见应用说明。掌握物理量之间的关系，理解单位，你就能征服物理。

1. Motion | 运动学

The equations of motion describe the behaviour of objects moving with constant acceleration in a straight line. You must be able to select the correct equation based on the known and unknown variables. Velocity, acceleration, displacement, and time are linked by these four fundamental formulas.

运动学方程描述了在直线上以恒定加速度运动的物体的行为。你必须能够根据已知量和未知量选择正确的方程。速度、加速度、位移和时间由这四个基本公式联系起来。

v = u + at

v = u + at
This equation relates final velocity (v) to initial velocity (u), acceleration (a), and time (t). Use it when time is given and acceleration is constant.

v = u + at
该方程将末速度 (v) 与初速度 (u)、加速度 (a) 和时间 (t) 联系起来。当已知时间且加速度恒定时使用。

s = ut + ½at²

s = ut + ½at²
Displacement (s) is calculated when initial velocity, time, and acceleration are known. This quadratic relationship is important for projectile motion components and stopping distances.

s = ut + ½at²
当已知初速度、时间和加速度时，计算位移 (s)。这个二次关系对于抛体运动的分量和刹车距离非常重要。

v² = u² + 2as

v² = u² + 2as
This is the perfect equation when time is not involved. It connects velocities, acceleration, and displacement. Useful for finding the final speed of a falling object or a braking vehicle.

v² = u² + 2as
当不涉及时间时，这是一个完美的方程。它连接了速度、加速度和位移。适用于求自由落体或刹车车辆的末速度。

v̄ = (u + v) / 2

v̄ = (u + v) / 2
Average velocity (v̄) for uniformly accelerated motion is the mean of initial and final velocities. You can then use s = v̄ t to find displacement.

v̄ = (u + v) / 2
匀加速运动的平均速度 (v̄) 是初速度和末速度的平均值。然后你可以使用 s = v̄ t 求位移。

2. Forces and Momentum | 力与动量

Newton’s laws provide the foundation for force and motion analysis. The concepts of resultant force, mass, acceleration, and momentum are central to both everyday mechanics and examination problem solving. Always pay attention to the direction of vectors.

牛顿定律为力和运动分析提供了基础。合力、质量、加速度和动量的概念是日常力学和考试解题的核心。务必注意矢量的方向。

F = ma

F = ma
Newton’s second law states that the resultant force (F) equals mass (m) multiplied by acceleration (a). The force is measured in newtons. This equation is used in countless IGCSE problems, from lifts to rockets.

F = ma
牛顿第二定律指出合力 (F) 等于质量 (m) 乘以加速度 (a)。力的单位是牛顿。这个方程在 IGCSE 题目中无处不在，从电梯到火箭。

W = mg

W = mg
Weight (W) is the force due to gravity. It equals mass (m) times gravitational field strength (g), typically 9.8 m/s² on Earth. Weight varies with location; mass does not.

W = mg
重量 (W) 是由重力引起的力。它等于质量 (m) 乘以重力场强度 (g)，在地球上通常为 9.8 m/s²。重量随位置变化，质量不变。

ρ = mv

ρ = mv
Momentum (ρ) is the product of mass and velocity. The symbol ρ (rho) is often used, but sometimes just p. Momentum is a vector quantity and is conserved in isolated systems.

ρ = mv
动量 (ρ) 是质量和速度的乘积。符号 ρ (rho) 常用，有时也用 p。动量是矢量，在孤立系统中守恒。

F = Δρ / Δt

F = Δρ / Δt
Resultant force equals the rate of change of momentum. This is another statement of Newton’s second law and is essential for understanding safety features like airbags and crumple zones.

F = Δρ / Δt
合力等于动量的变化率。这是牛顿第二定律的另一种表述，对于理解安全气囊和溃缩区等安全特性至关重要。

3. Energy, Work and Power | 能量、功与功率

Energy is a core concept that links all areas of physics. In IGCSE you need to be confident with the principle of conservation of energy, calculating work done, kinetic energy, gravitational potential energy, and power. Efficiency and renewable/non-renewable resources also draw on these equations.

能量是连接物理学各个领域的核心概念。在 IGCSE 中，你需要熟练掌握能量守恒定律，计算功、动能、重力势能以及功率。效率和可再生/不可再生资源也基于这些方程。

W = Fd

W = Fd
Work done (W) is the product of the force applied in the direction of movement and the distance (d) moved. Measured in joules. When the force is perpendicular to the displacement, no work is done.

W = Fd
功 (W) 是在运动方向施加的力与移动距离 (d) 的乘积。单位为焦耳。当力垂直于位移时，不做功。

Eₖ = ½mv²

Eₖ = ½mv²
Kinetic energy depends on mass and the square of the velocity. This quadratic relationship means doubling the speed quadruples the kinetic energy, a vital point in road safety.

Eₖ = ½mv²
动能取决于质量和速度的平方。这种平方关系意味着速度翻倍会使动能变为原来的四倍，这是道路安全中的一个关键点。

Eₚ = mgh

Eₚ = mgh
Gravitational potential energy (Eₚ) equals mass × gravitational field strength × height (h) above a reference level. Used in hydroelectric power, roller coasters, and pendulum problems.

Eₚ = mgh
重力势能 (Eₚ) 等于质量 × 重力场强度 × 参考水平以上的高度 (h)。用于水力发电、过山车和摆锤问题。

P = W / t or P = E / t

P = W / t 或 P = E / t
Power (P) is the rate of doing work or transferring energy. The unit is watt (W). A 60 W lamp transfers 60 joules of energy each second.

P = W / t 或 P = E / t
功率 (P) 是做功或传递能量的速率。单位是瓦特 (W)。一个 60 W 的灯泡每秒传递 60 焦耳的能量。

4. Pressure and Density | 压强与密度

Pressure, density, and their relationship in fluids are tested regularly in the IGCSE paper. You need to know how to calculate pressure from force and area, and how pressure changes with depth in a liquid. The simple ratio of mass to volume defines density.

压强、密度以及它们在流体中的关系是 IGCSE 试卷中的常考内容。你需要知道如何根据力和面积计算压强，以及液体中压强如何随深度变化。质量与体积的简单比值定义了密度。

ρ = m / V

ρ = m / V
Density (ρ) is mass per unit volume. The Greek letter rho is used. This fundamental property determines whether an object floats or sinks: an object with a density less than a fluid’s will float.

ρ = m / V
密度 (ρ) 是单位体积的质量。使用希腊字母 rho 表示。这个基本性质决定了物体的沉浮：密度小于流体的物体会漂浮。

p = F / A

p = F / A
Pressure (p) is force per unit area. It is measured in pascals (Pa). A small force over a small area can produce a very high pressure, which is why knives are sharp and stiletto heels can damage floors.

p = F / A
压强 (p) 是单位面积上的力。单位为帕斯卡 (Pa)。一个小力作用在小面积上可以产生很高的压强，这就是为什么刀是锋利的，而细高跟会损坏地板。

Δp = ρgΔh

Δp = ρgΔh
The pressure difference in a fluid column equals fluid density × gravitational field strength × height difference. This formula applies to barometers, manometers, and underwater pressure calculations.

Δp = ρgΔh
液柱中的压强差等于流体密度 × 重力场强度 × 高度差。此公式适用于气压计、压力计和水下压强的计算。

5. Thermal Physics | 热物理

Thermal physics formulae connect heat energy, temperature change, and changes of state. The specific heat capacity and latent heat equations are often tested together in practical questions about heating and cooling curves. The gas laws and the behaviour of molecules complete the picture.

热物理公式将热能、温度变化和状态变化联系起来。比热容和潜热方程经常在关于加热和冷却曲线的实践性问题中一起考查。气体定律和分子行为构成了完整的图景。

Q = mcΔθ

Q = mcΔθ
Thermal energy (Q) needed to raise the temperature equals mass × specific heat capacity (c) × temperature change (Δθ). Water has a high specific heat capacity, which makes it useful as a coolant and explains coastal climates.

Q = mcΔθ
升高温度所需的热能 (Q) 等于质量 × 比热容 (c) × 温度变化 (Δθ)。水具有很高的比热容，这使其可用作冷却剂并解释了沿海气候。

Q = mL

Q = mL
Energy needed to change state (at constant temperature) equals mass × specific latent heat (L). For melting, use specific latent heat of fusion; for boiling, use specific latent heat of vaporisation.

Q = mL
状态变化（在恒定温度下）所需的能量等于质量 × 比潜热 (L)。熔化时使用熔化比潜热；沸腾时使用汽化比潜热。

p₁V₁ = p₂V₂ (constant T)

p₁V₁ = p₂V₂ (恒温)
Boyle’s law for a fixed mass of gas at constant temperature: pressure is inversely proportional to volume. This is a key gas law often demonstrated with a syringe or a Boyle’s law apparatus.

p₁V₁ = p₂V₂ (恒温)
固定质量气体在恒温下的玻意耳定律：压强与体积成反比。这是经常用注射器或玻意耳定律仪器演示的关键气体定律。

6. Waves | 波动

The wave equation links wave speed, frequency, and wavelength. This single equation is applied to sound waves, water waves, and in the electromagnetic spectrum. Understanding how to use it in ripple tank experiments and with echo problems is essential.

波速方程将波速、频率和波长联系在一起。这一方程适用于声波、水波和电磁波谱。在波纹槽实验和回声问题中理解如何使用它至关重要。

v = fλ

v = fλ
Wave speed (v) equals frequency (f) multiplied by wavelength (λ). Frequency is in hertz (Hz). All electromagnetic waves travel at 3.0 × 10⁸ m/s in a vacuum. You can rearrange this to find any unknown.

v = fλ
波速 (v) 等于频率 (f) 乘以波长 (λ)。频率的单位是赫兹 (Hz)。所有电磁波在真空中都以 3.0 × 10⁸ m/s 的速度传播。你可以变形此公式求出任何未知量。

7. Optics | 光学

In optics, the law of reflection and the refractive index formula are cornerstones. You will need to know how to calculate refractive index from speeds and from angles, as well as the critical angle for total internal reflection. These formulas underpin fibre optics and lens behaviour.

在光学中，反射定律和折射率公式是基石。你需要知道如何根据速度和角度计算折射率，以及全内反射的临界角。这些公式是光纤和透镜行为的基础。

n = c / v

n = c / v
Refractive index (n) of a medium is the ratio of the speed of light in a vacuum (c) to the speed of light in the medium (v). This value is always greater than or equal to 1.

n = c / v
介质的折射率 (n) 是真空中的光速 (c) 与介质中的光速 (v) 之比。这个值总是大于或等于 1。

n = sin i / sin r

n = sin i / sin r
Snell’s law: refractive index can also be calculated from the angle of incidence (i) and angle of refraction (r) when light enters the medium from air (or vacuum). Remember that angles are measured from the normal.

n = sin i / sin r
斯涅尔定律：当光从空气（或真空）进入介质时，折射率也可以由入射角 (i) 和折射角 (r) 计算。记住角度是从法线测量的。

sin c = 1 / n

sin c = 1 / n
The critical angle (c) for total internal reflection satisfies sin c = 1/n. This occurs only when light travels from a denser to a less dense medium. Used in optical fibres and endoscopes.

sin c = 1 / n
全内反射的临界角 (c) 满足 sin c = 1/n。这仅当光从光密介质射向光疏介质时发生。用于光纤和内窥镜。

8. Electricity | 电学

Electrical circuits are central to the IGCSE physics exam. The relationships among charge, current, voltage, resistance, and power are expressed in a handful of equations. You must be able to apply them to series and parallel circuits, combining them with Ohm’s law and the power formulas.

电路是 IGCSE 物理考试的核心内容。电荷、电流、电压、电阻和功率之间的关系由少数几个方程表达。你必须能够将它们应用于串联和并联电路，并与欧姆定律和功率公式结合使用。

Q = It

Q = It
Electric charge (Q) transferred equals current (I) multiplied by time (t). Charge is measured in coulombs. This equation is fundamental for electrolysis and capacitor studies (though capacitors are not core IGCSE, the formula is given).

Q = It
转移的电荷 (Q) 等于电流 (I) 乘以时间 (t)。电荷的单位是库仑。该方程是电解和电容器研究的基础（尽管电容器不是 IGCSE 核心内容，但该公式会被给出）。

V = IR

V = IR
Ohm’s law: potential difference (V) across a conductor equals current (I) times resistance (R). Resistance is measured in ohms (Ω). The I-V graph for a resistor is linear only if temperature is constant.

V = IR
欧姆定律：导体两端的电势差 (V) 等于电流 (I) 乘以电阻 (R)。电阻的单位是欧姆 (Ω)。只有在温度恒定时，电阻器的 I-V 图才是线性的。

P = IV

P = IV
Power (P) in an electrical circuit equals current times voltage. This is the most general power formula. For a resistive component it can be combined with V = IR to give P = I²R or P = V²/R.

P = IV
电路中的功率 (P) 等于电流乘以电压。这是最通用的功率公式。对于电阻元件，它可以与 V = IR 结合得到 P = I²R 或 P = V²/R。

E = Pt = IVt

E = Pt = IVt
Electrical energy (E) transferred equals power × time. With P = IV, this becomes E = IVt. The kilowatt-hour (kWh) is a common unit of energy used in household electricity billing.

E = Pt = IVt
传递的电能 (E) 等于功率 × 时间。由 P = IV，可得 E = IVt。千瓦时 (kWh) 是家庭用电计费中常用的能量单位。

9. Electromagnetism | 电磁学

The interplay between electricity and magnetism yields the motor effect and electromagnetic induction. Transformer equations and the force on a current-carrying conductor are particularly important for the IGCSE. These formulas show how voltage and current are transformed, and how motors generate motion.

电与磁的相互作用产生了电动机效应和电磁感应。变压器方程以及载流导体所受的力对于 IGCSE 特别重要。这些公式展示了电压和电流如何变换，以及电动机如何产生运动。

Vₚ / Vₛ = Nₚ / Nₛ

Vₚ / Vₛ = Nₚ / Nₛ
For an ideal transformer, the ratio of the primary voltage (Vₚ) to the secondary voltage (Vₛ) equals the ratio of the number of turns in the primary coil (Nₚ) to the secondary coil (Nₛ). Step-up and step-down transformers follow this rule.

Vₚ / Vₛ = Nₚ / Nₛ
对于理想变压器，初级电压 (Vₚ) 与次级电压 (Vₛ) 之比等于初级线圈匝数 (Nₚ) 与次级线圈匝数 (Nₛ) 之比。升压和降压变压器都遵循此规则。

Vₚ Iₚ = Vₛ Iₛ (ideal)

Vₚ Iₚ = Vₛ Iₛ (理想情况)
Assuming 100% efficiency, the power input equals power output: Vₚ Iₚ = Vₛ Iₛ. In reality, some power is lost as heat due to resistance and eddy currents.

Vₚ Iₚ = Vₛ Iₛ (理想情况)
假设效率为 100%，输入功率等于输出功率：Vₚ Iₚ = Vₛ Iₛ。实际上，由于电阻和涡流，部分功率会以热量形式损失。

F = BIL (field perpendicular to conductor)

F = BIL (磁场垂直于导体)
The force (F) on a current-carrying conductor in a magnetic field equals magnetic flux density (B) × current (I) × length of conductor within the field (L). Fleming’s left-hand rule gives the direction of the force.

F = BIL (磁场垂直于导体)
磁场中载流导体所受的力 (F) 等于磁通密度 (B) × 电流 (I) × 导体在磁场中的长度 (L)。弗莱明左手定则给出了力的方向。

10. Atomic Physics and Radioactivity | 原子物理与放射性

Radioactive decay is random but follows a predictable pattern described by half-life. You may not need to use exponential decay formulas at IGCSE (graphical determination is common), but the basic arithmetic surrounding half-life, background count, and the types of radiation (alpha, beta, gamma) is essential. Nuclear equations balance mass and atomic numbers.

放射性衰变是随机的，但遵循由半衰期描述的可预测模式。在 IGCSE 阶段，你可能不需要使用指数衰变公式（通常用图解法），但围绕半衰期、本底计数以及辐射类型（α、β、γ）的基本算术是必不可少的。核反应方程要配平质量数和原子序数。

No specific standalone formula is normally required for half-life calculations beyond repeated division by two. However, you must be able to calculate the remaining mass or activity after a given number of half-lives:

除了反复除以 2 以外，通常不需要使用特定的半衰期公式。但是，你必须能够计算经过给定数量的半衰期后剩余的质量或活度：

remaining = initial × (½)ⁿ, where n = number of half-lives

remaining = initial × (½)ⁿ, 其中 n = 半衰期个数
If a sample has an initial activity of 800 Bq and a half-life of 2 days, after 6 days (3 half-lives) the activity will be 800 × (½)³ = 100 Bq. Background radiation must be subtracted first if applicable.

如果一个样品的初始活度是 800 Bq，半衰期为 2 天，那么经过 6 天（3 个半衰期）后，活度将是 800 × (½)³ = 100 Bq。如果适用，必须首先减去本底辐射。

Nuclear equations follow the conservation of mass number (A) and atomic number (Z). For alpha decay: ᴬₓX → ᴬ⁻⁴ₓ₋₂Y + ⁴₂He. For beta decay: ᴬₓX → ᴬₓ₊₁Y + ⁰₋₁e. You must be able to complete such equations.

核反应方程遵循质量数 (A) 和原子序数 (Z) 守恒。对于 α 衰变：ᴬₓX → ᴬ⁻⁴ₓ₋₂Y + ⁴₂He。对于 β 衰变：ᴬₓX → ᴬₓ₊₁Y + ⁰₋₁e。你必须能够完成这类方程。

11. Space Physics (Core only) | 空间物理（仅核心内容）

For those studying the Space Physics topic, a few key formulas and relationships are worth remembering. The orbital speed of a planet or satellite, and the link between orbital period and orbital distance, often appear in the extended syllabus but are also useful for core understanding. The equation for Hubble’s law is sometimes required.

对于学习空间物理专题的同学，有几个关键的公式和关系值得记住。行星或卫星的轨道速度，以及轨道周期与轨道距离之间的联系，经常出现在拓展大纲中，但对核心内容的理解也有用。哈勃定律的方程有时也会被要求使用。

v = 2πr / T

v = 2πr / T
Orbital speed (v) for a circular orbit equals the circumference (2πr) divided by the period (T). This simple relationship connects the radius of the orbit and the time for one complete revolution. It applies to planets, moons, and artificial satellites.

v = 2πr / T
圆形轨道的轨道速度 (v) 等于周长 (2πr) 除以周期 (T)。这个简单的关系连接了轨道半径和完整公转一次的时间。适用于行星、卫星和人造卫星。

v = H₀d (Hubble’s law)

v = H₀d (哈勃定律)
The speed at which a galaxy is moving away from us (v) is proportional to its distance (d) from us. H₀ is the Hubble constant. This provides evidence for the expansion of the Universe and the Big Bang theory.

v = H₀d (哈勃定律)
星系远离我们的速度 (v) 与其到我们的距离 (d) 成正比。H₀ 是哈勃常数。这为宇宙膨胀和大爆炸理论提供了证据。

12. Formula Summary Table | 公式速查表

The table below brings together all the essential IGCSE formulas in one place. Use it for quick revision. The topic columns will help you locate the equation you need when practising past papers.

下表将所有重要的 IGCSE 公式汇集在一起。可用于快速复习。主题列将帮助你在练习历年真题时找到所需的方程。

Topic / 主题	Formula / 公式	Units / 单位
Motion	v = u + at; s = ut + ½at²; v² = u² + 2as; v̄ = (u+v)/2	m/s, m, s, m/s²
Forces	F = ma; W = mg; ρ = mv; F = Δρ/Δt	N, kg, m/s², kg·m/s
Energy	W = Fd; Eₖ = ½mv²; Eₚ = mgh; P = W/t	J, N·m, W
Pressure / Density	ρ = m/V; p = F/A; Δp = ρgΔh	kg/m³, Pa, cm, m
Thermal	Q = mcΔθ; Q = mL; pV = constant	J, kg, °C, Pa, m³
Waves	v = fλ	m/s, Hz, m
Optics	n = c/v; n = sin i / sin r; sin c = 1/n	dimensionless
Electricity	Q = It; V = IR; P = IV; E = IVt	C, A, s, V, Ω, W
Electromagnetism	Vₚ/Vₛ = Nₚ/Nₛ; VₚIₚ = VₛIₛ; F = BIL	V, turns, N, T, A, m
Atomic	remaining = initial × (½)ⁿ	varies

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IGCSE CIE Physics Formula Handbook | IGCSE CIE 物理公式汇总手册