Leveling, angles and distances, traverse coordinates, area and earthwork.
NCEES lists these Surveying topics for the FE Civil: angles, distances and trigonometry; area computations; earthwork and volume computations; coordinate systems: state plane, latitude and longitude; leveling: differential, elevations, percent grades.
Choose any section below to get a free FE Civil practice problem. Work it with the FE Reference Handbook open, tap your answer, then check the solution.
Differential leveling: height of instrument HI = known elevation + backsight (BS); the elevation of the next point = HI − foresight (FS).
A level run starts at a benchmark of elevation 245.60 ft. Setup 1: BS 3.84 ft on the BM, FS 7.21 ft on TP1. Setup 2: BS 5.12 ft on TP1, FS 2.66 ft on TP2. Setup 3: BS 1.95 ft on TP2, FS 6.08 ft on point X. What is the elevation of X?
ΣBS = 3.84 + 5.12 + 1.95 = 10.91 ft. ΣFS = 7.21 + 2.66 + 6.08 = 15.95 ft. Elevation X = 245.60 + 10.91 − 15.95 = 240.56 ft.
Common trap: (B) Reverses the signs: subtracts the backsights and adds the foresights.
LevelingDifferential LevelingCurvature and RefractionStadiaThat was 1 of 4 problems in this section. The full course has the lesson, a worked example and every problem. Start your 3-day free trial →
A bearing is an acute angle from north or south toward east or west; an azimuth is measured clockwise from north (0° to 360°).
What is the azimuth of the bearing S 35°20′ E?
S θ E → 180° − θ = 180° − 35°20′ = 144°40′.
Common trap: (B) That is the bearing angle itself.
AzimuthBearingAngle BalanceHorizontal Curve StakingThat was 1 of 4 problems in this section. The full course has the lesson, a worked example and every problem. Start your 3-day free trial →
For a line of length L and azimuth α: latitude (northing change) = L cos α; departure (easting change) = L sin α.
Point A has coordinates N 5,000.00, E 3,000.00. Line AB is 412.36 ft at bearing N 38°15′ E, and line BC is 285.90 ft at bearing S 62°40′ E. What are the coordinates of C?
AB: Lat = 412.36 cos 38°15′ = +323.83; Dep = 412.36 sin 38°15′ = +255.29. BC: Lat = −285.90 cos 62°40′ = −131.28; Dep = +285.90 sin 62°40′ = +253.98. NC = 5,000.00 + 323.83 − 131.28 = 5,192.56; EC = 3,000.00 + 255.29 + 253.98 = N 5,192.56, E 3,509.27.
Common trap: (B) Swaps sine and cosine, computing departures as latitudes.
Latitude and DepartureTraverse ClosureCompass RuleCoordinate AreaThat was 1 of 4 problems in this section. The full course has the lesson, a worked example and every problem. Start your 3-day free trial →
Average end area volume: V = L(A1 + A2)/2, converted to cubic yards by dividing by 27.
A channel cut has a 40 ft bottom width and 2H:1V side slopes. At station 10+00 the cut is 5 ft deep, and at station 11+00 it is 7 ft deep. What is the excavation volume between them by the prismoidal formula?
A1 = (40 + 2·5)(5) = 250 ft²; A2 = (40 + 2·7)(7) = 378 ft²; mid-section depth 6 ft: Am = (40 + 2·6)(6) = 312 ft². V = (100/6)[250 + 4(312) + 378] = 31,267 ft³; /27 = 1,158.0 CY.
Common trap: (B) Uses the average end area method (or averages the end areas to get Am, which gives the same result).
Average End AreaPrismoidal FormulaSimpson's RulePercent GradeThat was 1 of 4 problems in this section. The full course has the lesson, a worked example and every problem. Start your 3-day free trial →
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