KS3 OCR Geography: Formulas & Theorems Quick Reference Handbook | KS3 OCR 地理：公式定理速查手册

📚 KS3 OCR Geography: Formulas & Theorems Quick Reference Handbook | KS3 OCR 地理：公式定理速查手册

Geography isn’t just about memorising places – it’s about measuring, calculating and interpreting the world. This quick reference handbook brings together the essential formulas, calculation rules and graphical theorems that appear throughout the KS3 OCR Geography course. Keep it close to build confidence with map skills, population data, rivers and climate analysis, and make your answers precise and exam-ready.

地理学习不单是记住地名，更是测量、计算和解读世界。这份速查手册汇编了 KS3 OCR 地理课程中必须掌握的公式、计算法则和图表定理。随身查阅，可助你自信应对地图技能、人口数据、河流与气候分析，让答题更精确、更贴合考试要求。

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1. Map Scale | 比例尺

Map scale expresses the relationship between a distance on the map and the corresponding distance on the ground. It can be presented as a statement (e.g. 1 cm represents 1 km), a linear scale bar or a representative fraction (RF) such as 1:50 000.

地图比例尺表示图上距离与实地距离的关系。它可以用文字说明（如 1 厘米代表 1 公里）、直线比例尺或数字比例尺（如 1:50 000）三种方式呈现。

The core formula transfers any map measurement into real-world length once both values use the same unit:

核心公式在单位统一的前提下将任何图上量测转换为实地长度：

Scale = Map Distance ÷ Ground Distance

When converting, always start by writing the ground distance in the same unit as the map measurement. For a 1:25 000 map, 1 cm on the map equals 25 000 cm on the ground, which simplifies to 250 m or 0.25 km.

换算时首先要将实地距离化为与图上距离相同的单位。在 1:25 000 地图上，图上 1 厘米等于实地 25 000 厘米，即 250 米或 0.25 公里。

Useful conversions to remember:
1 km = 1000 m = 100 000 cm
1 m = 100 cm

常用单位换算：
1 公里 = 1000 米 = 100 000 厘米
1 米 = 100 厘米

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2. Straight-Line Distance | 直线距离

To find the straight-line distance between two points on a map, measure the distance with a ruler in centimetres and apply the scale. The formula for ground distance is:

要量算地图上两点间的直线距离，先用直尺量出厘米数，再套用比例尺。计算实地距离的公式为：

Ground Distance = Map Distance × Scale Factor

The scale factor is the denominator of the representative fraction. On a 1:50 000 map, a measured 4 cm line gives 4 × 50 000 = 200 000 cm, which is 2000 m or 2 km. Always convert the final answer into a sensible unit such as metres or kilometres.

比例系数即数字比例尺的分母。在 1:50 000 地图上，量得 4 厘米线段，计算为 4 × 50 000 = 200 000 厘米，即 2000 米或 2 公里。最后务必将答案换算为合理单位，如米或公里。

When measuring the winding course of a river or a road, use a piece of string or the edge of a piece of paper. Mark the turns, straighten the string, measure its length against the ruler and then apply the scale factor. This gives a reasonable estimate of the curved distance.

若量测蜿蜒的河流或道路，可用细绳或纸条边缘沿路线摆放，标出弯折处，拉直后量取长度，再乘以比例系数。这样可得到较准确的曲线距离估算值。

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3. Six-Figure Grid References | 六位数网格参考

Six-figure grid references locate a point within a 100 m by 100 m square on Ordnance Survey maps. The golden rule is “along the corridor and up the stairs” – eastings first, then northings.

六位数网格参考可将地点定位在英国地形测量局地图上 100 米见方的方格内。黄金法则是“先沿走廊走，再上楼”——先读东向坐标，后读北向坐标。

Procedure:
1. Identify the two-digit easting number on the left of the grid square.
2. Mentally divide the space between that easting and the next into ten equal parts; count how many tenths the point lies across – this gives the third digit.
3. Repeat with the two-digit northing below the square to obtain the sixth digit.

操作步骤：
1. 找出方格左侧的两位数东向坐标。
2. 将该东方向与下一条网格线之间十等分，数出目标点在第几个十分之一处，得到第三位数。
3. 同样处理方格下方的两位数北向坐标，得到第六位数。

Example: if a point is inside square 27 (easting) 43 (northing), lies 4/10 across and 7/10 up, the full reference is 274 437. Always write eastings first, then a space, then northings.

示例：某点位于东向 27、北向 43 的方格内，向东 4/10、向北 7/10，则六位参考为 274 437。务必先写东向坐标，空一格再写北向坐标。

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4. Measuring Area on a Map | 地图面积测算

The area of a feature on the ground can be estimated from its map outline. Because scale applies to length, area scales by the square of the scale factor. The relationship is:

实地地物面积可由图上轮廓估算得出。因比例尺作用于长度，面积的比例需使用比例系数的平方。关系式为：

Ground Area = Map Area × (Scale Factor)²

If a lake covers 6 cm² on a 1:25 000 map, begin by realising that 1 cm² on the map represents (25 000)² = 625 000 000 cm² on the ground. Multiply: 6 × 625 000 000 = 3 750 000 000 cm². Convert to m² by dividing by 10 000 (since 1 m² = 10 000 cm²), which gives 375 000 m². It is often easier to convert the ground equivalent of 1 cm into metres first: 1 cm = 250 m, so 1 cm² = 62 500 m²; then 6 × 62 500 = 375 000 m².

若某湖泊在 1:25 000 图上面积为 6 平方厘米，先理解图上 1 平方厘米相当于实地 (25 000)² = 625 000 000 平方厘米。计算 6 × 625 000 000 = 3 750 000 000 平方厘米。除以 10 000 换算为平方米（1 平方米 = 10 000 平方厘米），即得 375 000 平方米。更简便的做法是先将 1 厘米代表的实地长度化为米：1 厘米 = 250 米，则 1 平方厘米 = 62 500 平方米；再用 6 × 62 500 = 375 000 平方米。

An alternative method for irregular shapes is to overlay a grid of small squares (e.g. 1 cm × 1 cm). Count full squares, combine part-squares into whole ones, and multiply the total number of squares by the ground area each square represents.

测量不规则图形面积的另一种方法是用小方格网格（如 1 厘米 × 1 厘米）覆盖。数出完整方格，将不完整方格凑整，再用方格总数乘以每个方格所代表的实地面积。

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5. Compass Bearings | 罗盘方位角

A compass bearing is the clockwise angle measured from true north (000°) or grid north on a map. Bearings are always given as three figures, e.g. 045° for north-east, 225° for south-west.

罗盘方位角是从真北（000°）或图上网格北顺时针量得的角度。方位角总以三位数字表示，如东北为 045°，西南为 225°。

Bearing = Clockwise angle from North (000° to 360°)

To measure a bearing on a map, place a protractor with its centre over the starting point and the 0° mark pointing to grid north. Read the angle where the line to the destination crosses the protractor scale. If the line points backwards, measure the acute angle and adjust: bearing = measured angle if forward, or add/subtract 180° if measuring the opposite direction.

在图上量取方位角时，将量角器中心对准起点，0° 刻度指向网格北。读取连接目标点直线所穿过的刻度值。若目标在后方，可先量出锐角，再通过加减 180° 求得正确方位角。

Always double-check whether you are working with grid north or magnetic north. In KS3, most bearings will be grid bearings taken directly from the easting grid lines.

务必确认你使用的是网格北还是磁北。KS3 阶段大多数方位角是以东向网格线为基准的网格方位角。

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6. Vertical Exaggeration | 垂直夸大

When drawing a cross-section from a contour map, the vertical scale is often enlarged to make relief features visible. Vertical exaggeration (VE) expresses how many times the vertical scale is larger than the horizontal scale.

根据等高线图绘制剖面时，为让地形起伏更明显，垂直比例尺往往被放大。垂直夸大（VE）表示垂直比例尺是水平比例尺的多少倍。

VE = Vertical Scale ÷ Horizontal Scale

Both scales must be expressed as representative fractions or as a unit ratio. If the horizontal scale is 1:50 000 and the vertical scale of the cross-section is 1 cm represents 100 m (i.e. 1:10 000), then VE = (1/10 000) ÷ (1/50 000) = 5. This means the heights are stretched five times, making slopes appear steeper than they really are.

两个比例尺都需写成分数比例或单位比例形式。若水平比例尺为 1:50 000，剖面垂直比例尺为 1 厘米表示 100 米（即 1:10 000），则 VE = (1/10 000) ÷ (1/50 000) = 5。这意味着高度被放大了 5 倍，剖面坡度比实际陡峭。

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7. Gradient | 坡度/梯度

Gradient compares the vertical change in height to the horizontal distance between two points. It is often expressed as a ratio 1:N or as a percentage.

坡度是两点间的高差与水平距离之比，常用 1:N 的比值或百分数表示。

Gradient = Vertical Interval (VI) ÷ Horizontal Equivalent (HE)

Vertical Interval is the difference in height between two contours or points. Horizontal Equivalent is the ground distance between them, measured along a straight line. Both must be in the same unit. If a hilltop rises 120 m over a distance of 600 m, Gradient = 120 ÷ 600 = 0.2, which simplifies to 1 in 5 (1:5). Always write the ratio with the vertical interval as 1.

高差是两条等高线或两点之间的高度差。水平距离是它们之间的直线实地距离。两者单位须统一。若山顶在 600 米水平距离内上升 120 米，坡度 = 120 ÷ 600 = 0.2，化简为 1:5。比值始终将高差化为 1。

Gradient can also be given as a percentage: multiply the decimal result by 100. In the example above, 0.2 × 100 = 20 %. In geography, steeper slopes have higher gradient percentages and smaller second numbers in the ratio.

坡度也可用百分数表示：将小数结果乘以 100。如上例 0.2 × 100 = 20%。在地理中，坡度越大，百分数越大，比值中第二个数字越小。

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8. River Discharge | 河流流量

River discharge is the volume of water passing a given point in the channel each second. It links the channel’s cross-sectional area and the flow velocity.

河流流量是每秒通过河道某断面的水量，其大小取决于过水断面面积与流速。

Discharge (Q) = Cross-sectional Area (A) × Velocity (V)

In the field, velocity is measured with a flow meter or float, and cross-sectional area is calculated by multiplying channel width by average depth. All measurements must be in consistent metric units: area in square metres (m²), velocity in metres per second (m/s), giving discharge in cubic metres per second (cumecs, m³/s).

田野调查中，流速用流速仪或浮标测得，过水断面面积由河宽乘以平均水深求得。所有测量必须统一公制单位：面积用平方米（m²），流速用米/秒（m/s），所得流量单位为立方米/秒（m³/s，又称 cumecs）。

Example: a stream 4 m wide and 0.5 m average depth has A = 4 × 0.5 = 2 m². If the velocity is 0.8 m/s, then Q = 2 × 0.8 = 1.6 cumecs. This formula helps explain why a river’s discharge increases downstream as width and depth grow.

示例：某小河宽 4 米、平均水深 0.5 米，则 A = 4 × 0.5 = 2 平方米。若流速为 0.8 米/秒，则 Q = 2 × 0.8 = 1.6 立方米/秒。这一公式也有助于解释为何下游流量随宽度和深度增加而变大。

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9. Population Density | 人口密度

Population density describes how crowded an area is, calculated as the number of people per unit area, usually per square kilometre.

人口密度用于描述某区域的拥挤程度，以单位面积的人口数表示，通常为每平方公里人数。

Population Density = Total Population ÷ Area (km²)

Make sure the area is in square kilometres. If the area is given in square metres or hectares, convert first: 1 km² = 1 000 000 m²; 1 km² = 100 hectares. A city of 2 million people covering 500 km² has a density of 2 000 000 ÷ 500 = 4000 people per km².

务必确保面积单位为平方公里。若面积以平方米或公顷给出，须先换算：1 平方公里 = 1 000 000 平方米；1 平方公里 = 100 公顷。一座拥有 200 万人口、面积 500 平方公里的城市，其人口密度为 2 000 000 ÷ 500 = 4000 人/平方公里。

Population density maps and choropleth shading allow geographers to compare the distribution of people globally. High densities often reflect fertile land, economic opportunities or historical urban growth.

人口密度图和分区统计着色图可帮助地理学者比较全球人口分布。高密度常反映肥沃土地、经济机遇或历史城市发展。

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10. Population Change | 人口变化

Population change is driven by two main components: natural change (births minus deaths) and net migration (immigration minus emigration). The essential formulas are:

人口变化主要由两大因素驱动：自然变动（出生减死亡）和净迁移（迁入减迁出）。核心公式为：

Natural Increase = Birth Rate – Death Rate

Net Migration = Immigration – Emigration

Total Population Growth = Natural Increase + Net Migration

Rates are usually expressed per 1000 people per year. If a country has a birth rate of 18 per 1000 and a death rate of 7 per 1000, its natural increase is 11 per 1000, or 1.1 %. This figure can be combined with net migration to understand overall demographic trends.

比率通常以每年每千人表示。若某国出生率为 18‰，死亡率为 7‰，其自然增长率为 11‰，即 1.1%。将此数字与净迁移率结合，即可理解整体人口趋势。

Demographers present these components using the demographic balancing equation: Population at end = Population at start + Births – Deaths + Immigration – Emigration. Always keep track of all four flows to explain GCSE case studies.

人口学家用人口平衡方程表示：期末人口 = 期初人口 + 出生 – 死亡 + 迁入 – 迁出。解释 GCSE 案例时，须完整追踪这四个变量。

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11. Doubling Time | 人口翻倍时间

Doubling time estimates how many years it will take for a population to double in size, assuming a constant annual growth rate. The simplest calculation is the “Rule of 70”:

人口翻倍时间用于估算在年增长率保持不变的条件下，人口规模翻一番所需的年数。最简便的算法是“70 法则”：

Doubling Time (years) = 70 ÷ Annual Growth Rate (%)

For example, a population growing at 2 % per year will double in approximately 70 ÷ 2 = 35 years. The rule works because the natural logarithm of 2 is about 0.693, and multiplying by 100 gives roughly 70. It is an approximation that geographers use to discuss rates of urbanisation and resource demand.

例如，年增长率为 2% 的人口约在 70 ÷ 2 = 35 年后翻倍。该法则源于 2 的自然对数约 0.693，乘 100 取近似值 70。地理学家用它探讨城市化速度和资源需求。

Doubling time falls as the growth rate rises. A rate of 3.5 % gives a doubling time of just 20 years, highlighting the urgency of planning in rapidly growing regions. Always check that the growth rate is entered as a percentage, not a decimal.

增长率越高，翻倍时间越短。3.5% 的增长率对应仅 20 年的翻倍时间，突显了高速增长地区规划的紧迫性。使用时务必确认增长率以百分数而非小数代入。

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12. Climate Graph Calculations | 气候图计算

Climate graphs combine monthly temperature and precipitation data to reveal seasonal patterns. Several straightforward calculations help summarise the data:

气候图将各月气温与降水数据结合，揭示季节规律。以下几个简单计算可概括数据特征：

Mean Annual Temperature = Sum of 12 Monthly Temperatures ÷ 12

Annual Temperature Range = Hottest Month Mean – Coldest Month Mean

Total Annual Precipitation = Sum of 12 Monthly Precipitation Values

For example, a station with monthly temperatures ranging from 5 °C in January to 25 °C in July has an annual range of 20 °C. A total precipitation of 850 mm spread unevenly across the year might suggest a dry season. These figures help classify climates as equatorial, Mediterranean or temperate.

例如，某测站 1 月均温 5 °C，7 月均温 25 °C，则年较差为 20 °C。年总降水量 850 毫米若分布不均，可能指示旱季存在。这些数据可帮助划分赤道气候、地中海气候或温带气候。

When drawing a climate graph, always use a line for temperature (plotted on the left vertical axis) and bars for precipitation (on the right axis). Label axes clearly and include units. Calculation of averages and ranges allows accurate comparison between different climate regions.

绘制气候图时，用折线表示气温（左纵轴），柱状图表示降水（右纵轴）。坐标轴须清楚标注单位。通过计算平均值与较差，可对不同气候区进行精确比较。

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