📚 IGCSE WJEC Geography Formula & Theorem Quick Reference | IGCSE WJEC 地理公式定理速查手册
Designed for IGCSE WJEC Geography candidates, this quick reference compiles the essential formulas, ratios, and quantitative skills required across key topics such as population dynamics, river processes, map work, and hazard management. Master these calculations to boost your exam performance and fieldwork analysis skills.
专为IGCSE WJEC地理考生设计，本速查手册汇集了人口动态、河流过程、地图技能和灾害管理等重要主题所需的必备公式、比率和定量技能。掌握这些计算，可有效提升考试成绩与实地考察分析能力。
1. Map Scale and Distance | 地图比例尺与距离
A fundamental skill in map work is converting between map distance and real-world ground distance. The three forms are interchangeable: Scale = Map Distance ÷ Ground Distance. Always express both distances in the same units before calculating.
地图工作的基本技能是在图距与实地距离之间转换。三者关系为：比例尺 = 图距 ÷ 实地距离。计算前务必保持两距离单位一致。
For linear scales on a map, use the formula: Ground Distance = Map Distance ÷ Scale. For example, on a 1:50 000 map, 4 cm on the map represents 4 cm × 50 000 = 200 000 cm, which is 2 km on the ground.
若使用地图上的直线比例尺，可用公式：实地距离 = 图距 ÷ 比例尺。例如，在1:50 000地图上，图上4 cm代表实地4 cm × 50 000 = 200 000 cm，即2 km。
2. Gradient and Slope | 梯度与坡度
Gradient measures the steepness of a slope, commonly used when interpreting contour lines or river long profiles. It is the ratio of vertical interval to horizontal equivalent: Gradient = Vertical Interval (VI) ÷ Horizontal Equivalent (HE). A gradient of 1:25 means for every 25 metres horizontally, the land rises by 1 metre.
梯度用于衡量坡度的陡缓，常用于判读等高线或河流纵剖面。它是垂直间隔与水平距离的比值：梯度 = 垂直高差 (VI) ÷ 水平距离 (HE)。梯度1:25表示水平距离每25米，上升1米。
To express slope as a percentage, multiply the ratio by 100: Slope % = (VI ÷ HE) × 100. Both VI and HE must be in the same units.
以百分比表示坡度时，将比值乘以100：坡度% = (VI ÷ HE) × 100。计算时垂直高差与水平距离须采用相同单位。
3. Population Density | 人口密度
Population density shows how crowded a place is and is vital for comparing settlement patterns. It is calculated simply as: Population Density = Total Population ÷ Land Area (usually km²). High density may indicate urban areas; low density often reflects rural or harsh environments.
人口密度反映一个地方的拥挤程度，对比较聚落形态至关重要。计算公式简单：人口密度 = 总人口 ÷ 土地面积（常用km²）。高密度往往指城市地区，低密度则常代表乡村或环境严酷地区。
Always check that the area is given in square kilometres before dividing. If the area is provided in hectares or square miles, convert first (1 km² = 100 ha; 1 mile² ≈ 2.59 km²).
计算前务必确认面积单位为平方千米。若以公顷或平方英里给出，需先换算（1 km² = 100 ha；1 mile² ≈ 2.59 km²）。
4. Birth Rate, Death Rate and Natural Increase | 出生率、死亡率与自然增长率
These demographic rates are expressed per 1000 population per year and are essential for analysing population change. The birth rate is: Birth Rate = (Number of live births ÷ Total population) × 1000. The death rate uses a similar formula: Death Rate = (Number of deaths ÷ Total population) × 1000.
这些人口统计比率以每年每千人为单位，是分析人口变化的基础。出生率公式：出生率 = (活产婴儿数 ÷ 总人口) × 1000。死亡率公式类似：死亡率 = (死亡人数 ÷ 总人口) × 1000。
Natural increase (or natural decrease) is the difference between birth rate and death rate, excluding migration: Rate of Natural Increase = Birth Rate – Death Rate. This is often shown as a percentage by dividing the difference by 10.
自然增长（或自然减少）是出生率与死亡率之差，不包括迁移影响：自然增长率 = 出生率 – 死亡率。通常将该差值除以10以转换为百分比。
5. Net Migration Rate | 净迁移率
Migration can dramatically alter a population’s size and structure. The net migration rate is calculated as: Net Migration Rate = ((Immigrants – Emigrants) ÷ Total population) × 1000. A positive value indicates net in-migration; a negative value means net out-migration.
迁移能显著改变人口规模与结构。净迁移率的计算公式为：净迁移率 = ((迁入人数 – 迁出人数) ÷ 总人口) × 1000。正值表示净迁入，负值表示净迁出。
Total population change combines natural increase and net migration: Population Change = (Births – Deaths) + (Immigrants – Emigrants). This gives the absolute change over a period, which can then be used to update the base population.
总人口变动综合了自然增长与净迁移：人口变动量 = (出生 – 死亡) + (迁入 – 迁出)。该公式得出一定时期内的绝对变化，可据此更新人口基数。
6. Population Doubling Time (Rule of 70) | 人口倍增时间（70法则）
A quick way to estimate how long it will take for a population to double, assuming a constant growth rate, is the Rule of 70: Doubling Time (years) = 70 ÷ Growth Rate (%). The growth rate must be the annual percentage increase.
在增长率恒定的前提下，快速估算人口翻倍所需时间可用70法则：倍增时间（年）= 70 ÷ 增长率(%)。增长率须取年百分比增幅。
For example, a country growing at 2% per year will double its population in approximately 70 ÷ 2 = 35 years. This rule applies to any exponential growth, such as resource consumption.
例如，年增长率为2%的国家，人口将在大约70 ÷ 2 = 35年内翻倍。该法则适用于任何指数增长，如资源消耗。
7. River Discharge | 河流流量
Discharge is the volume of water flowing through a river channel per second, measured in cubic metres per second (cumecs). The fundamental formula is: Discharge (Q) = Cross-sectional Area (A) × Mean Velocity (V). Field measurements of width, depth and velocity are needed to calculate A and V.
流量是每秒通过河道的水体体积，单位为立方米/秒（cumecs）。基本公式为：流量 (Q) = 断面面积 (A) × 平均流速 (V)。需实地测量河宽、水深和流速以计算A和V。
Velocity is often measured using a flow meter or by timing a float over a known distance. Mean velocity may be taken at 0.6 of the depth if the stream is not too shallow. Remember that A is the wetted cross-section, not the total channel depth under a bridge.
流速常用流速仪或通过测量浮标通过已知距离的时间来获取。若水流不过浅，可在水深0.6倍处测平均流速。注意断面面积指过水断面，而非桥下全深度。
8. Cross-sectional Area of a Channel | 河道断面面积
To find river discharge, you must first estimate the cross-sectional area. For a simple rectangular approximation: Area = Width × Mean Depth. For irregular channels, divide the width into several vertical sections, measure depth at each, and use the trapezoidal rule or average depth.
计算河流流量前需先估算断面面积。简单的矩形近似下：面积 = 河宽 × 平均水深。对于不规则河道，可将河宽分成若干垂直截面，逐一测量水深，再用梯形法则或求平均水深。
A common field method is: Mean Depth = (d₁ + d₂ + … + dₙ) ÷ n, where d is depth at regular intervals. Multiply mean depth by width for a quick estimate. For more accuracy, calculate area as the sum of trapezoid segments.
常用野外方法：平均水深 = (d₁ + d₂ + … + dₙ) ÷ n，其中d为等间距点的水深。将平均水深乘以河宽即可快速估算。若需更精确，可将面积视为多个梯形面积之和。
9. Speed, Time and Distance in Transport | 交通中的速度、时间与距离
Understanding accessibility in human geography often requires calculating travel time or average speed. Use the relationship: Speed = Distance ÷ Time. From this, Distance = Speed × Time and Time = Distance ÷ Speed.
人文地理中理解可达性常需计算行程时间或平均速度。运用关系式：速度 = 距离 ÷ 时间。由此可得距离 = 速度 × 时间，时间 = 距离 ÷ 速度。
When analysing transport networks, map distance and average road speed can be combined to find travel time. Always convert units consistently, e.g. distance in km, time in hours, speed in km/h.
分析交通网络时，可将地图距离与平均道路速度结合求得行程时间。务必统一单位，例如距离用km，时间用小时，速度用km/h。
10. Percentage Urban / Urbanisation Level | 城市化水平（城市人口百分比）
The level of urbanisation indicates the proportion of a country’s population living in urban areas. It is expressed as: Urbanisation Level (%) = (Urban Population ÷ Total Population) × 100. This indicator is central to studying changing places and economic development.
城市化水平表示一国居住在城市地区的人口比例。公式为：城市化水平 (%) = (城市人口 ÷ 总人口) × 100。该指标是研究变化中的场所与经济发展的核心。
The rate of urbanisation is the speed at which this percentage is changing. Compare figures over time to classify countries as experiencing rapid or slow urban growth. Note that a high percentage urban does not necessarily equal a large urban population in absolute terms.
城市化速度指该百分比变化快慢。可对比不同时期数据判断一国正经历快速还是缓慢城市化。注意，高城市化百分比并不等于绝对数量上的大城人口。
11. Risk and Hazard Formula | 灾害风险公式
In studying tectonic and climatic hazards, risk is often conceptualised using a simple formula: Risk = Hazard × Vulnerability ÷ Capacity to Cope. Hazard is the potentially dangerous event; vulnerability refers to the susceptibility of people; and capacity includes resources and preparedness.
在学习地震、气候等灾害时，风险常由一简单公式表达：风险 = 致灾因子 × 脆弱性 ÷ 应对能力。致灾因子指潜在危险事件；脆弱性指人群易损程度；应对能力包括资源与备灾水平。
This model helps explain why an earthquake of the same magnitude can have very different impacts in two locations. Reducing vulnerability or increasing capacity lowers risk, even if the hazard event itself cannot be prevented.
该模型有助于解释为何同震级的地震在两地的灾情大相径庭。降低脆弱性或增强应对能力可减小风险，即便致灾事件本身无法阻止。
12. Economic Indicators: GDP per Capita | 经济指标：人均GDP
Gross Domestic Product (GDP) per capita is a widely used measure of a country’s average economic output per person. It is calculated as: GDP per capita = Total GDP ÷ Population. This is a key indicator in the ‘Changing Economies’ theme, used to classify countries into HICs, MICs and LICs.
人均国内生产总值（人均GDP）是衡量一国平均每人经济产出的常用指标。计算公式为：人均GDP = 总GDP ÷ 人口。这是在“变化中的经济体”主题中将国家分为高收入、中等收入和低收入的关键指标。
When comparing data, remember that GDP per capita does not reflect income distribution. For a fuller picture, combine with other development indicators such as the Human Development Index (HDI) or Gini coefficient.
进行数据比较时应注意，人均GDP并不反映收入分配状况。为获得全面印象，可结合其他发展指标，如人类发展指数（HDI）或基尼系数。
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