📚 GCSE OCR Geography: Formula & Theorem Quick Reference Handbook | GCSE OCR 地理：公式定理速查手册
This quick reference handbook brings together all the essential formulae and key conceptual models you need for the GCSE OCR Geography examinations. From river processes and hydrological cycles to population dynamics and development indicators, each entry is presented with a clear formula, a worked example, and concise explanation. Mastering these tools will strengthen your data-response questions, fieldwork analysis, and numerical reasoning under timed conditions.
这本速查手册汇集了 GCSE OCR 地理考试所需的所有基本公式和关键概念模型。从河流过程、水文循环到人口动态和发展指标，每个条目都配有清晰的公式、计算示例和简明解释。掌握这些工具能强化你的数据应答、实地考察分析和限时计算能力。
1. Gradient (Slope) of a River | 河流坡度计算
Gradient is a measure of a river’s steepness, traditionally expressed as a ratio or a decimal. It is fundamental in understanding velocity changes and erosive power along a long profile. For fieldwork, you often calculate gradient between two points along a channel using vertical rise and horizontal distance.
坡度是衡量河流陡峭程度的指标，通常以比值或小数表示。它对理解沿河流纵剖面的流速变化和侵蚀力至关重要。在野外考察中，你通常利用垂直落差和水平距离来计算沿河道两点间的坡度。
Gradient = Vertical Rise (m) ÷ Horizontal Distance (m)
If a stream falls 6 metres over a 200-metre reach, the gradient is 6 ÷ 200 = 0.03 or 3%. This value helps predict whether the flow is likely to be turbulent (steeper) or more laminar (gentler). On OS maps, gradient can be estimated using contour spacing.
如果一条溪流在 200 米河段内下降 6 米，坡度为 6 ÷ 200 = 0.03 或 3%。这个数值有助于预测水流是湍急（较陡）还是较平缓。在 OS 地图上，可以通过等高线间距估算坡度。
2. River Discharge | 河流流量
Discharge (Q) is the volume of water flowing through a cross-section of a river per unit time. It is a core concept for flood risk analysis and links directly to the Bradshaw model. Discharge is calculated by multiplying the channel’s cross-sectional area by mean velocity.
流量（Q）是单位时间内流过河道某一横截面的水体积。这是洪水风险分析的核心概念，并与布拉德肖模型直接相关。流量由河道横截面积乘以平均流速计算得出。
Discharge (Q) = Cross-sectional Area (A) × Mean Velocity (V)
The standard unit for discharge is cumecs (cubic metres per second, m³/s). In fieldwork, you might use a float to estimate velocity and a tape measure to find width and depth for area. Remember, as river width, depth, and velocity all increase downstream, discharge also increases.
流量的标准单位是立方米每秒（cumecs, m³/s）。在野外考察中，你可以用浮标估算流速，用卷尺测量宽度和深度以求得面积。请记住，随着河道宽度、深度和流速向下游增加，流量也会增大。
3. Cross-Sectional Area of a Channel | 河道横截面积
To calculate discharge, you must first determine the cross-sectional area of the channel. While natural channels are irregular, a simplified approach multiplies channel width by mean depth. In a field transect, area is often approximated by summing several depth readings and averaging them.
要计算流量，首先必须确定河道横截面积。虽然天然河道形状不规则，但简化方法是用河道宽度乘以平均水深。在实地横断面中，常常通过多次水深测量取平均值来近似计算面积。
Cross-sectional Area (A) = Channel Width (w) × Mean Depth (d̄)
For example, if a river is 8 metres wide and the arithmetic mean depth from five verticals is 0.45 m, the area is 8 × 0.45 = 3.6 m². Multiplying by the measured velocity (e.g., 0.7 m/s) then gives a discharge of 2.52 m³/s. This method underpins many GCSE field studies.
例如，如果一条河宽 8 米，从五条垂线测得的算术平均水深为 0.45 米，则面积为 8 × 0.45 = 3.6 平方米。再乘以实测流速（如 0.7 米/秒），得到流量 2.52 立方米/秒。这一方法是许多 GCSE 野外研究的基础。
4. Drainage Basin Water Balance | 流域水平衡
The water balance equation expresses the way inputs and outputs of water interact within a drainage basin over a given period. It is a simple but powerful tool for understanding whether a catchment is storing or losing water and for interpreting hydrographs.
水平衡方程表达了在一定时期内流域内水分的输入与输出相互作用的方式。它是一个简单但有力的工具，可用于了解集水区是在蓄水还是失水，也可用于解释水位过程线。
Precipitation (P) = Runoff (R) + Evapotranspiration (E) + Change in Storage (ΔS)
In this formula, runoff includes both surface and channel flow. Evapotranspiration covers evaporation from water and soil plus transpiration by vegetation. The storage term (ΔS) can be positive (surplus, increasing groundwater/soil moisture) or negative (deficit). Practise applying this equation to explain seasonal flooding or drought.
在这个公式中，径流包括地表径流和河道水流。蒸发蒸腾涵盖水面和土壤蒸发以及植被蒸腾。存储变量（ΔS）可以为正（盈余，增加地下水/土壤湿度）或负（亏缺）。练习运用此方程解释季节性洪水或干旱。
5. Birth Rate, Death Rate, and Natural Increase | 出生率、死亡率和自然增长
Demographic rates are fundamental to population geography and feature regularly in OCR exam questions. Birth rate and death rate are expressed per 1000 people per year, while natural increase can be given as an absolute number or a rate. Understanding these allows you to analyse the Demographic Transition Model.
人口统计率是人口地理学的基础，在 OCR 考试题目中经常出现。出生率和死亡率表示为每年每千人，而自然增长可以用绝对数字或比率给出。理解这些率可以让你分析人口转变模型。
Birth Rate (per 1000) = (Number of Live Births ÷ Total Population) × 1000
Death Rate (per 1000) = (Number of Deaths ÷ Total Population) × 1000
Natural Increase Rate (per 1000) = Birth Rate − Death Rate
If a country has a birth rate of 22‰ and a death rate of 7‰, its natural increase rate is 15 per 1000, or 1.5% per annum. Absolute natural increase = Births − Deaths. Be careful with units: the rates are per thousand, not per hundred.
如果一个国家的出生率为 22‰，死亡率为 7‰，其自然增长率为每千人 15，即每年 1.5%。绝对自然增长 = 出生人数 − 死亡人数。注意单位：这些率是千分比，而非百分比。
6. Population Density | 人口密度
Population density is a crude but widely used indicator of how crowded a place is. It is essential for comparing regions, explaining distribution patterns, and linking to resources and land use. The formula takes total population and land area in consistent units.
人口密度是一个粗略但广泛使用的指标，用于衡量一个地方的拥挤程度。它对于比较区域、解释分布模式以及联系资源与土地用途至关重要。该公式采用总人口与土地面积，单位需保持一致。
Population Density = Total Population ÷ Land Area (km²)
For example, the UK has around 67 million people and an area of about 243,610 km², giving a density of approximately 275 people per km². Remember that density is an average; it can mask sparse highlands versus dense urban cores. Always use reliable data and state the unit clearly.
例如，英国约有 6700 万人口，面积约 243,610 平方公里，得出密度约为每平方公里 275 人。请记住，密度是一个平均值；它可能掩盖稀疏的高地与密集的城市核心之间的差异。始终使用可靠数据并明确标注单位。
7. Urbanisation Rate | 城市化率
Urbanisation, the increasing proportion of a country’s population living in urban areas, is a key trend for both ACs, EDCs and LIDCs. The urbanisation rate measures this balance and helps explain economic development and migration patterns.
城市化，即一国人口中居住在城市地区比例的增加，是 AC、EDC 和 LIDC 的共同关键趋势。城市化率衡量这一比重，有助于解释经济发展和迁移模式。
Urbanisation Rate (%) = (Urban Population ÷ Total Population) × 100
If a city has an urban population of 1.2 million within a total national population of 4 million, the urbanisation rate is (1.2m ÷ 4m) × 100 = 30%. While some countries remain largely rural, rates above 80% are common in high-income nations. Note the rate of urbanisation (the speed of change) is different from the level of urbanisation.
如果某国城市人口为 120 万，总人口为 400 万，城市化率为 (120万 ÷ 400万) × 100 = 30%。尽管一些国家仍以农村为主，但在高收入国家，城市化率超过 80% 很常见。请注意，城市化速度（变化的速度）与城市化水平是不同的概念。
8. Dependency Ratio | 抚养比
The dependency ratio is a measure of the economic burden on the productive population. It compares the number of people likely to be economically dependent (young and elderly) with the working-age population. This formula is directly linked to population pyramids and issues of ageing or youthful populations.
抚养比是衡量劳动人口经济负担的指标。它将可能的受抚养人口（少儿和老人）与劳动年龄人口进行比较。该公式与人口金字塔、老龄化或年轻化人口问题直接相关。
Dependency Ratio (%) = [(Pop₀₋₁₄ + Pop₆₅₊) ÷ Pop₁₅₋₆₄] × 100
For a country with 18 million under 15, 4 million aged 65+, and 38 million aged 15–64, the dependency ratio is (22m ÷ 38m) × 100 ≈ 57.9%. This means for every 100 working-age people there are about 58 dependants. Higher ratios imply greater pressure on public services such as healthcare and pensions.
对于一个有 1800 万 15 岁以下、400 万 65 岁以上和 3800 万 15-64 岁人口的国家，抚养比为 (2200万 ÷ 3800万) × 100 ≈ 57.9%。这意味着每 100 名劳动年龄人口对应约 58 名受抚养者。抚养比越高，意味着医疗和养老金等公共服务的压力越大。
9. Gross Domestic Product (GDP) per Capita | 人均国内生产总值
GDP per capita is a standard economic indicator used to compare the average wealth of different countries. It does not show income distribution but is fundamental for development indicators such as HDI. The calculation divides total GDP by mid-year population.
人均 GDP 是用于比较不同国家平均财富的标准经济指标。它不体现收入分配，但对人类发展指数 (HDI) 等发展指标至关重要。计算方法是用国内生产总值除以年中人口数。
GDP per Capita = Total GDP (US$) ÷ Total Population
If a country has a GDP of US$ 960 billion and a population of 80 million, GDP per capita is $12,000. When analysing data, remember that values can be given in nominal terms or adjusted for purchasing power parity (PPP). Always note whether the figure is in US dollars and the source year.
如果某国 GDP 为 9600 亿美元，人口为 8000 万，人均 GDP 为 12,000 美元。分析数据时，请记住数值可以按名义价值给出，也可以按购买力平价 (PPP) 调整。始终注明数字是否为美元以及来源年份。
10. Rate of Coastal Erosion or Deposition | 海岸侵蚀或沉积速率
Measuring the rate of land loss or gain along a coastline is a common fieldwork and exam topic. Erosion rate is typically expressed as the horizontal retreat of the cliff line per year, while deposition can be measured as beach height or width increase.
测量海岸线土地流失或增长的速率是常见的野外考察和考试主题。侵蚀速率通常表示为每年悬崖线的水平后退距离，而沉积速率则可通过海滩高度或宽度的增加来衡量。
Erosion Rate = Horizontal Retreat (m) ÷ Time Period (years)
For instance, if a cliff has retreated 4.2 metres over a monitor period of 30 years, the average annual erosion rate is 4.2 ÷ 30 = 0.14 m/year. This can be compared with a critical threshold to decide whether hard engineering is justified. Be sure to use consistent date comparisons from maps or GPS data.
例如，如果一个悬崖在 30 年监测期内后退了 4.2 米，则年均侵蚀速率为 4.2 ÷ 30 = 0.14 米/年。可以将其与临界阈值进行比较，以判断硬防护工程是否合理。务必使用来自地图或 GPS 数据的一致日期进行比较。
11. Bradshaw Model Overview | 布拉德肖模型概述
The Bradshaw model is a conceptual theorem that describes expected changes in river characteristics from source to mouth. While not a mathematical formula, it is a key ‘rule’ used to predict trends in channel variables. OCR exam questions often ask you to evaluate whether fieldwork data fits the model.
布拉德肖模型是一个概念性定理，描述了从源头到河口河流特征预期的变化。尽管不是数学公式，但它是一个用于预测河道变量趋势的关键‘规则’。OCR 考试常要求你评估野外数据是否符合该模型。
The model predicts the following downstream trends: discharge, channel width, channel depth, mean velocity, and sediment load all increase. In contrast, gradient and bedload particle size decrease. Use this as a checklist when presenting your river investigation conclusions.
该模型预测了以下下游趋势：流量、河道宽度、河道深度、平均流速以及输沙量均增加。相反，坡度和推移质粒径会减小。在呈现河流调查结论时，可将此用作核对清单。
Note that real river data may deviate because of tributaries, geology, and human intervention. Always give reasons when anomalies occur. Representing the model as a set of arrow diagrams or a table can strengthen your evaluation.
请注意，由于支流、地质和人为干预，实际河流数据可能会偏离模型。出现异常时，务必说明原因。用箭头示意图或表格来表现模型可以增强你的评价力。
12. Population Doubling Time (Rule of 70) | 人口倍增时间（70 法则）
Doubling time provides a strikingly clear way of communicating the speed of population growth. The Rule of 70 offers a quick estimate: divide 70 by the annual percentage growth rate. The result tells you approximately how many years it would take for a population to double at current growth.
倍增时间提供了一种极其清晰的方式来传达人口增长的速度。70 法则可进行快速估算：用 70 除以年增长率百分比。结果会告诉你，按当前增长速度，人口大约需要多少年才能翻一番。
Doubling Time (years) = 70 ÷ Annual Growth Rate (%)
For example, a country with a 2.5% annual growth rate has a doubling time of 70 ÷ 2.5 = 28 years. This formula assumes exponential growth and works best for rates between 1% and 10%. It is a useful planning tool for resources, housing, and food security.
例如，一个年增长率为 2.5% 的国家，其倍增时间为 70 ÷ 2.5 = 28 年。该公式假设呈指数增长，最适用于 1% 至 10% 之间的增长率。它是资源、住房和粮食安全规划的有用工具。
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