📚 SQA Geography Formulas & Theorems Quick Reference | SQA 地理公式定理速查手册
This quick reference handbook provides a structured overview of essential formulas, statistical methods, spatial models and physical theorems required for Year 13 SQA Geography. Whether you are tackling human geography data analysis, river basin hydrology or map interpretation in your Higher or Advanced Higher course, these concise notes will help you recall the quantitative and conceptual tools you need under exam conditions. Each entry is presented as a bilingual pair, with the key equation or principle clearly stated and explained.
本速查手册系统梳理了 Year 13 SQA 地理课程所必备的公式、统计方法、空间模型和自然地理定理。无论你正在应对人文地理数据分析、流域水文学还是地图判读，这些简洁的双语笔记都能帮助你在备考和考试时快速调用所需的定量工具与概念原理。
1. Population Indicators | 人口指标
Crude Birth Rate (CBR) = (Number of live births in a year / Total mid-year population) × 1000. It measures the number of births per 1000 people in a given population.
粗出生率（CBR）=（年内活产数 / 年中总人口）× 1000。该指标衡量每千人中的出生人数。
Crude Death Rate (CDR) = (Number of deaths in a year / Total mid-year population) × 1000. Similarly, the rate is expressed per 1000 people.
粗死亡率（CDR）=（年内死亡人数 / 年中总人口）× 1000。同样以每千人为单位。
Natural Increase Rate = CBR – CDR. A positive value indicates population growth from births and deaths alone, excluding migration.
自然增长率 = 粗出生率 – 粗死亡率。正值表示仅由出生和死亡引起的人口增长，不包括迁移。
Doubling Time (years) ≈ 70 / (Annual growth rate %). This rule of 70 provides a quick estimate of how long it takes for a population to double in size.
人口倍增时间（年）≈ 70 /（年增长率 %）。这条“70法则”可快速估算人口规模翻倍所需的年数。
2. Urban Models & Theorems | 城市模型与定理
Burgess’s Concentric Zone Model (1925) conceptualises the city as a series of concentric rings radiating outwards from the CBD. The model is based on land value and accessibility patterns observed in early 20th-century Chicago.
伯吉斯的同心圆模型（1925年）将城市概念化为一组从中央商务区向外扩展的同心圆带。该模型基于20世纪早期芝加哥观察到的土地价值和通达性模式。
Hoyt’s Sector Model (1939) argues that cities develop in wedges or sectors along transport routes, not just in rings. High-rent residential areas, for example, often follow arterial roads or railways.
霍伊特的扇形模型（1939年）主张城市沿交通线路呈楔形或扇形发展，而不仅仅是环形。例如，高租金居住区常沿着主干道或铁路分布。
The Central Place Theorem (Christaller, 1933) explains the size, number and distribution of settlements based on centralised provision of goods and services. The range (maximum distance consumers travel) and threshold (minimum population to support a service) determine settlement hierarchy.
中心地理论（克里斯塔勒，1933年）以商品和服务的集中供给为基础，解释了聚落的规模、数量和分布。商品的销售范围（消费者愿意出行的最大距离）和门槛人口（维持服务的最低人口）决定了聚落等级。
The Bid‑Rent Theory states that land value decreases with distance from the CBD. Different land users (retail, industry, residential) compete for accessibility, producing a rent gradient.
竞租理论认为，土地价值随距离 CBD 的增加而下降。不同的土地利用者（零售、工业、居住）竞争通达性，形成租金梯度。
3. River Discharge & Hydraulic Radius | 河流流量与水力半径
Discharge (Q) = Cross‑sectional Area (A) × Mean Velocity (V), often written as Q = A × V. Discharge is measured in cubic metres per second (m³ s⁻¹) and represents the volume of water flowing past a point in a given time.
流量（Q）= 横截面积（A）× 平均流速（V），通常写作 Q = A × V。流量单位为立方米每秒（m³ s⁻¹），表示单位时间内流经某一点的水量。
Hydraulic Radius (R) = A / Wetted Perimeter. The hydraulic radius influences channel efficiency; a larger R generally indicates less frictional resistance and higher velocity.
水力半径（R）= 横截面积 / 湿周。水力半径影响河道效率；较大的 R 通常意味着较小的摩擦阻力和较高的流速。
Manning’s Equation: V = (R²/³ × S¹/²) / n, where S is slope and n is Manning’s roughness coefficient. This is used to estimate velocity in open channels.
曼宁公式：V = (R²/³ × S¹/²) / n，其中 S 为坡降，n 为曼宁糙率系数。该公式用于估算明渠流速。
4. Statistical Measures: Mean, Median, Mode | 统计量度：平均值、中位数、众数
Mean (x̄) = Σx / n. The arithmetic mean is the sum of all values divided by the number of data points. It is sensitive to extreme values (outliers).
平均值（x̄）= Σx / n。算术平均值是所有数值之和除以数据个数。它对极端值（异常值）很敏感。
Median is the middle value when data are arranged in rank order. For an even number of observations, it is the average of the two central values. The median is robust to outliers.
中位数是将数据排序后位于中间位置的数值。当观测值个数为偶数时，取最中间两个数的平均值。中位数不受异常值影响。
Mode is the most frequently occurring value in a data set. A data set can have one mode (unimodal), two modes (bimodal) or more.
众数是数据集中出现频率最高的值。数据集可有一个众数（单峰）、两个众数（双峰）或更多。
5. Measures of Dispersion: Range, Interquartile Range, Standard Deviation | 离散度量：极差、四分位距、标准差
Range = Maximum value – Minimum value. The range gives a simple measure of spread but is heavily influenced by a single extreme value.
极差 = 最大值 – 最小值。极差提供了简单的离散程度度量，但极易受到单个极端值影响。
Interquartile Range (IQR) = Q3 – Q1, where Q1 is the lower quartile (25th percentile) and Q3 is the upper quartile (75th percentile). The IQR describes the spread of the middle 50% of the data and is more resistant to outliers.
四分位距（IQR）= Q3 – Q1，其中 Q1 为下四分位数（第25百分位数），Q3 为上四分位数（第75百分位数）。IQR 描述了中间50%数据的分布范围，抗异常值性更强。
Standard Deviation (σ for population, s for sample) measures the average distance of each data point from the mean. s = √[ Σ(x – x̄)² / (n – 1) ]. A low standard deviation indicates data points are clustered closely around the mean.
标准差（总体记为 σ，样本记为 s）衡量各数据点与平均值之间的平均距离。s = √[ Σ(x – x̄)² / (n – 1) ]。低标准差意味着数据点紧密聚集在平均值附近。
6. Spearman’s Rank Correlation Coefficient | 斯皮尔曼等级相关系数
Spearman’s rₛ = 1 – [ 6 Σd² / (n(n² – 1)) ], where d is the difference between the ranks of each paired observation and n is the number of pairs. It tests the strength and direction of a monotonic relationship between two variables.
斯皮尔曼 rₛ = 1 – [ 6 Σd² / (n(n² – 1)) ]，其中 d 为每对观测值的位次差，n 为配对数量。该系数检验两个变量之间单调关系的强度和方向。
Values of rₛ range from –1 (perfect negative correlation) to +1 (perfect positive correlation). A value of 0 suggests no correlation. In SQA coursework, you must test significance of rₛ against critical values at the 95% or 99% confidence level.
rₛ 取值范围从 –1（完全负相关）到 +1（完全正相关）。0 表示无相关。在 SQA 课程作业中，必须将 rₛ 与临界值对照以检验其显著性，通常使用95%或99%的置信水平。
7. Chi-Squared Test | 卡方检验
Chi-squared (χ²) = Σ [ (O – E)² / E ], where O represents observed frequency and E represents expected frequency. The test assesses whether there is a significant association between two categorical variables.
卡方 χ² = Σ [ (O – E)² / E ]，其中 O 为观测频数，E 为期望频数。该检验评估两个分类变量之间是否存在显著关联。
Degrees of freedom (df) = (number of rows – 1) × (number of columns – 1). You compare the calculated χ² value to the critical value for the given degrees of freedom and significance level (usually 0.05).
自由度（df）=（行数 – 1）×（列数 – 1）。将计算所得的 χ² 值与给定自由度和显著性水平（通常为0.05）下的临界值进行比较。
If χ² calculated > χ² critical, reject the null hypothesis and conclude that there is a statistically significant association.
若 χ² 计算值 > χ² 临界值，则拒绝原假设，得出存在统计显著关联的结论。
8. Geographical Information Systems (GIS) Formulae | 地理信息系统公式
Scale = Map Distance / Ground Distance. For example, a scale of 1:50 000 means 1 cm on the map represents 50 000 cm (500 m) on the ground.
比例尺 = 图上距离 / 实地距离。例如，比例尺1:50 000 表示图上1厘米代表实地50 000厘米（500米）。
Pixel Resolution (in remote sensing) = Ground Distance / Number of Pixels. A finer resolution (smaller ground cell size) provides more detail but requires more storage space.
像元分辨率（遥感）= 地面距离 / 像元数量。更精细的分辨率（更小的地面像元尺寸）提供更多细节，但需要更多存储空间。
Normalised Difference Vegetation Index (NDVI) = (NIR – Red) / (NIR + Red). NDVI values range from –1 to +1; healthy dense vegetation typically yields values close to +1.
归一化植被指数（NDVI）=（近红外 – 红）/（近红外 + 红）。NDVI 值介于 –1 至 +1 之间；健康茂密的植被通常产生接近 +1 的值。
9. Map Skills: Gradient, Area, Relief | 地图技能：坡度、面积、地形
Gradient = Vertical Interval (VI) / Horizontal Equivalent (HE). It is often expressed as a ratio (e.g., 1:20) or as a fraction. On Ordnance Survey maps, height change is read from contours, and horizontal distance is measured using the scale bar.
坡度 = 垂直高差（VI）/ 水平距离（HE）。常以比率（如1:20）或分数表示。在地形图上，高度变化从等高线读取，水平距离用比例尺测量。
Area can be estimated using the grid square method: count full and partial squares within the feature boundary, multiply by the ground area represented by one square. On a 1:25 000 map, a 1 km grid square represents 1 km².
面积可用网格法估算：计算地物边界内的完整和部分格网数，乘以每个格网所代表的实地面积。在1:25 000地图上，1 km格网代表1 km²。
Relief refers to the difference in height between the highest and lowest points in a given area. Cross‑sections are constructed by plotting contour crossings along a transect line.
地形起伏指某区域内最高点与最低点之间的高度差。地形剖面图通过沿着剖面线标绘等高线交点绘制。
10. Demographic Transition Model & Rostow’s Model | 人口转变模型与罗斯托模型
The Demographic Transition Model (DTM) describes population change over time in five stages, from high fluctuating birth and death rates (Stage 1) to low and stable rates (Stage 5). The key theorem is that as societies develop from pre-industrial to industrialised, a population first experiences falling death rates, then falling birth rates, leading to temporary rapid growth.
人口转变模型（DTM）通过五个阶段描述人口随时间的变化：从高出生率、高死亡率波动的第一阶段到低而稳定的第五阶段。其核心定理是，随着社会从工业化前向工业化发展，人口首先经历死亡率下降，随后出生率下降，从而导致暂时的快速增长。
The formula for population change: Population change = (Births – Deaths) + (Immigration – Emigration). The DTM focuses on natural change, while the full equation adds migration.
人口变化公式：人口变化 =（出生数 – 死亡数）+（迁入 – 迁出）。人口转变模型侧重于自然变化，而完整公式加入了迁移因素。
Rostow’s Modernisation Model (1960) outlines five stages of economic growth: traditional society, preconditions for take‑off, take‑off, drive to maturity, and age of high mass consumption. It provides a theoretical structure for understanding development pathways.
罗斯托现代化模型（1960年）概述了经济增长的五个阶段：传统社会、起飞前提条件、起飞、走向成熟和高额大众消费时代。它为理解发展路径提供了理论结构。
11. Soil Erosion: Universal Soil Loss Equation (USLE) | 土壤侵蚀：通用土壤流失方程
USLE: A = R × K × LS × C × P, where A is the estimated average annual soil loss (tonnes per hectare per year). R is the rainfall erosivity factor, K is the soil erodibility factor, LS is the slope length‑gradient factor, C is the cover‑management factor, and P is the support practice factor.
通用土壤流失方程：A = R × K × LS × C × P，其中 A 为估算的年均土壤流失量（吨/公顷/年）。R 为降雨侵蚀力因子，K 为土壤可蚀性因子，LS 为坡长‑坡度因子，C 为覆盖与管理因子，P 为水土保持措施因子。
This equation helps geographers quantify the impact of different land management practices on soil loss. Even a small change in slope gradient can significantly increase LS, demonstrating the non‑linear relationship between topography and erosion.
该方程有助于地理学家量化不同土地管理实践对土壤流失的影响。坡度的微小变化即可显著增大 LS 值，表明地形与侵蚀之间存在非线性关系。
12. Climate & Weather Formulae: Lapse Rates, Relative Humidity | 气候与天气公式：气温递减率、相对湿度
Environmental Lapse Rate (ELR): The observed decrease of air temperature with altitude in the troposphere, averaging 6.5 °C per 1000 m. It is variable and depends on local conditions.
环境气温递减率（ELR）：对流层中观测到的气温随高度下降的速率，平均为每1000米下降6.5°C。该值可变，取决于局地条件。
Dry Adiabatic Lapse Rate (DALR) = 9.8 °C per 1000 m. This is the rate at which a parcel of unsaturated air cools as it rises. Saturated Adiabatic Lapse Rate (SALR) ≈ 5.5 °C per 1000 m, slower due to the release of latent heat during condensation.
干绝热递减率（DALR）= 每1000米9.8°C。这是未饱和空气块上升时的冷却速率。湿绝热递减率（SALR）约为每1000米5.5°C，因凝结释放潜热而较慢。
Relative Humidity (RH) = (Actual water vapour content / Saturation water vapour content at the same temperature) × 100%. RH indicates how close the air is to saturation, which influences cloud formation and precipitation.
相对湿度（RH）=（实际水汽含量 / 同温度下的饱和水汽含量）× 100%。相对湿度表示空气接近饱和的程度，影响云的生成和降水。
Wind chill formula (modern approach) calculates the cooling effect felt on exposed skin as a function of wind speed and temperature. In the UK, the Met Office uses the Joint Action Group for Temperature Indices (JAG/TI) formula.
风寒温度（现代方法）以风速和温度的函数计算裸露皮肤感受到的冷却效应。英国气象局采用 JAG/TI 公式。
Published by TutorHao | Geography Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导Cancel reply