FS Exam Preparation

Comprehensive preparation for the Fundamentals of Surveying (FS) exam. 7 modules covering all 7 exam domains with 60 in-depth topics.

Progress0/60

Lesson 1

Map Concepts & Cartography

Learning Objectives

After completing this topic, you should be able to:

Define map scale and convert between scale representations
Explain the relationship between map scale and map accuracy
Describe standard map symbology conventions
Understand the National Map Accuracy Standards (NMAS)
Calculate ground distances and areas from map measurements
Identify the components of a well-designed map

Overview

Cartography is the science and art of mapmaking. While surveyors are not typically cartographers, they must understand fundamental map concepts to create accurate, clear, and standards-compliant deliverables. The FS exam tests basic cartographic principles including scale, accuracy standards, symbology, and map design.

Key Concepts

Figure FS.2.1 — Map Scale Types

Map Scale

$Figure FS.2.1b — Map scale: representative fraction, verbal, and graphic forms; scale conversions; large vs. small scale$

Map scale is the ratio between a distance on the map and the corresponding distance on the ground. It can be expressed in three ways:

Representative Fraction (RF):

A unitless ratio, e.g., 1:24,000
Means 1 unit on the map equals 24,000 of the same units on the ground
1 inch on the map = 24,000 inches (2,000 feet) on the ground

Verbal scale:

Expressed in words: "1 inch equals 200 feet" or "1 cm equals 50 meters"
Easy to understand but unit-specific

Graphic (bar) scale:

A line drawn on the map with distances marked
Remains accurate even if the map is enlarged or reduced (unlike RF and verbal scales)

Scale conversions:

To convert between representations:

1 inch = 200 feet is equivalent to 1:2,400 (because 200 ft x 12 in/ft = 2,400 in)
1:50,000 means 1 cm on the map = 500 m on the ground (50,000 cm = 500 m)

Large scale vs. small scale:

Large scale maps (e.g., 1:500, 1:1,200) show a small area with great detail -- typical for engineering and survey plans
Small scale maps (e.g., 1:250,000, 1:1,000,000) show a large area with little detail -- typical for regional and reference maps
Remember: a larger RF denominator means a smaller scale

National Map Accuracy Standards (NMAS)

Figure FS.2.1c — NMAS accuracy standards (legacy) and ASPRS RMSE-based criteria; map design elements; standard map symbology

The NMAS (1947) established accuracy requirements for published maps:

Horizontal accuracy:

For maps at scales larger than 1:20,000: 90% of well-defined features shall be within 1/30 inch (0.85 mm) of their true position at map scale
For maps at scales of 1:20,000 or smaller: 90% within 1/50 inch (0.5 mm)

Vertical accuracy:

Not more than 10% of elevations tested shall be in error by more than one-half the contour interval, and none can exceed the interval (Ghilani & Wolf, Elementary Surveying 13th ed., p. 506)

Example: At 1:2,400 scale, the horizontal accuracy requirement is:

1/30 inch x 2,400 = 80 inches = 6.67 ft (2.03 m)

ASPRS Positional Accuracy Standards for Digital Geospatial Data (Edition 2, 2023) have largely replaced NMAS for modern mapping, using RMSE-based criteria at the 95% confidence level.

Map Design Elements

Figure FS.2.1e — Ten standard map elements (title, scale, north arrow, etc.)

A complete, professional map should include:

Element	Purpose
Title	Identifies the subject and location
Scale	Shows the relationship between map and ground distances
North arrow	Indicates orientation; specifies true, magnetic, or grid north
Legend	Explains all symbols, line types, and abbreviations used
Date	When the map was prepared or when the data was collected
Coordinate grid or tick marks	Enables position referencing
Source information	Credits data sources, surveys, and references
Projection and datum	Identifies the mathematical basis for the map
Contour interval	States the elevation difference between contour lines
Surveyor/cartographer identification	Professional responsible for the product

Map Symbology

Standard survey and topographic maps use established symbology conventions:

Line types:

Solid lines: Property boundaries, building outlines, roads
Dashed lines: Hidden features, easement lines, proposed improvements
Dotted lines: Section lines, fence lines
Dash-dot-dash: Centerlines

Point symbols:

Triangles: Triangulation/control stations
Circles with cross: Traverse points
Squares: Benchmarks
Various symbols for trees, utility poles, manholes, fire hydrants, etc.

Area symbols:

Hatch patterns for water, wetlands, wooded areas
Color fills for zoning, land use, or soil types

Common wrong path — scaling area by the linear scale factor. When computing ground area from a measured map area, students frequently multiply by the linear scale factor (e.g., 200 for a 1"=200' map) instead of the squared scale factor (200² = 40,000). The correct relationship: linear map dimensions scale by the scale factor; area scales by the square of the scale factor. A map area of 2 square inches at 1"=100' is 2 × 100² = 20,000 sq ft, NOT 2 × 100 = 200 sq ft. This is a fundamental mathematical property (area scales as length squared) but it trips students on the exam regularly. Similarly, volume would scale as length cubed — so a model-space cubic foot at a 1:100 model scale represents 100³ = 1,000,000 cubic feet of ground. Always cube or square the scale factor as appropriate for the dimension of the measurement.

Quick retrieval check — try before reading on.

▶A subdivision plat at 1"=60' shows a lot with a measured area of 5.5 square inches. What is the ground area in square feet and in acres?

Scale factor for area = 60² = 3,600 sq ft per sq inch.

Ground area = 5.5 sq in × 3,600 sq ft/sq in = 19,800 sq ft.

In acres: 19,800 / 43,560 = 0.454 acres (about 0.45 acre).

Common mistakes:

Multiplying by 60 linearly: 5.5 × 60 = 330 sq ft (wrong by factor of 60 — represents what a 5.5-inch long line would be, not an area)
Forgetting to convert to acres: 19,800 sq ft without the acre conversion leaves the answer in a less useful unit for property comparisons

Area scales as the square of the linear scale factor; volume would scale as the cube. This is not a surveying convention — it is basic geometry.

Calculating Ground Distances and Areas from Maps

Figure FS.2.1d — Area scales as the square of the linear scale factor

Distance: Measure the map distance, then multiply by the scale factor.

Map distance: 3.5 inches; Scale: 1 inch = 100 feet
Ground distance: 3.5 x 100 = 350 feet

Area: Map areas scale by the square of the scale factor.

Map area: 2.4 square inches; Scale: 1 inch = 200 feet
Ground area: 2.4 x (200)^2 = 2.4 x 40,000 = 96,000 sq ft (approximately 2.2 acres)

Exam Tips

Large scale = large detail, small area (e.g., 1:500); small scale = small detail, large area (e.g., 1:1,000,000)
When converting scale, keep units consistent -- convert feet to inches or meters to centimeters as needed
A graphic (bar) scale remains accurate when the map is enlarged or reduced; an RF does not
NMAS horizontal accuracy is 1/30 inch at map scale for large-scale maps
NMAS vertical accuracy is one-half the contour interval
Area scales by the square of the linear scale factor -- this is a common exam calculation
Know the standard map elements (title, scale, north arrow, legend, date)
The FS exam may give you a map scale and ask you to calculate ground distance or area

FS Exam Preparation

Module 1: Surveying Processes & Methods

Module 2: Mapping Processes & Methods

Module 3: Boundary Law & Real Property

Module 4: Surveying Principles & Geodesy

Module 5: Survey Computations

Module 6: Business Concepts

Module 7: Applied Math & Statistics