Formula reference

Cheat sheet

87 formulas and rules across 18 topics, each with the variables, the trap the exam sets, and a question to try it on. On exam day the NCEES FS Reference Handbook is on screen; this is for learning what to look up and how to use it.

Get the official handbook. It is free but login-only: create a MyNCEES account at account.ncees.org, then open Common Tasks → Useful Documents → View Reference Handbooks. NCEES does not allow it to be reposted, so it is not mirrored here.

Units and conversions Angles, bearings, azimuths Triangles and slope reduction Traverse computations Areas Horizontal curves Vertical curves Leveling Taping and EDM Errors and statistics Weights, least squares, accuracy standards GNSS Geodesy and State Plane Photogrammetry and remote sensing Map accuracy and GIS Public Land Survey System Business and licensure math Georgia minimum technical standards (Rule 180-7)

Units and conversionsNCEES · Applied Mathematics

Two feet

1 US survey ft = 12003937 m · 1 international ft = 0.3048 m exactly

They differ by 2 ppm. Negligible on a tape, but 2 ft on a 1,000,000 ft State Plane coordinate, 4.6 ft on Georgia West's 700,000 m false easting.

Georgia switched to the international foot on 1 July 2022 (O.C.G.A. 44-4-27): 1 m = 3.280839895 ft.

Try itmath 1 · easy math 2 · medium geodesy datums 23 · hard ga mts 15 · medium

Gunter's chain

1 chain = 66 ft = 100 links = 4 rods · 1 link = 0.66 ft · 80 chains = 1 mile

The trap is the 100 ft engineer's chain. If a deed says chains, it means 66 ft.

Try itmath 3 · medium plss 1 · easy plane calcs 16 · easy

Area units

1 acre = 10 square chains = 43,560 ft² · 1 section = 640 acres = 1 mi² · 1 township = 36 sections = 23,040 acres

Chains × chains ÷ 10 = acres. Feet × feet ÷ 43,560 = acres.

Try itmath 4 · easy plss 2 · easy plss 3 · easy

Stationing

12+34.56 = 1,234.56 ft from 0+00 · one full station = 100 ft

Distance between stations is plain subtraction once both are in feet. Off-by-one-station is the usual slip.

Try itmath 5 · easy

Degrees, minutes, seconds

decimal = D + M60 + S3600 · 1° = 60′ = 3600″ · 1 rad = 206,265″

Borrow 60, not 100, when subtracting: 180°00′ − 152°37′ = 179°60′ − 152°37′ = 27°23′.

Try itmath 6 · easy math 11 · medium

Small angles (ρ″ = 206,265)

offset = D × θ″206,265 · θ″ = 206,265 × eD

D: sight distance
e: linear offset (centering error, bubble displacement)

A 5 mm centering error at 50 m is 21″; at 500 m it is 2″. Short sights amplify centering error.

Try itmath 7 · medium field data 20 · medium field data 24 · hard

Angles, bearings, azimuthsNCEES · Survey Computations

Bearing ↔ azimuth

NE: Az = β · SE: Az = 180° − β · SW: Az = 180° + β · NW: Az = 360° − β

β: bearing angle, always measured from N or S toward E or W, 0° to 90°

Back azimuth = Az ± 180°. Back bearing keeps the angle and flips both letters.

Try itmath 8 · easy math 9 · medium plane calcs 1 · easy plane calcs 2 · easy

Angle sums in a closed traverse

Σ interior = (n − 2) × 180° · Σ exterior = (n + 2) × 180° · Σ deflection = 360°

n: number of sides

Deflection angle at a station = 180° − interior angle.

Try itmath 10 · easy plane calcs 3 · easy field data 6 · easy

Allowable angular misclosure

c = K √n · K (FGCS): 1st 1.7″ · 2nd I 3.0″ · 2nd II 4.5″ · 3rd I 10″ · 3rd II 12″

n: number of angles (stations)

√n, never n. Distribute the misclosure equally per angle unless told otherwise.

Try itplane calcs 4 · easy field data 25 · hard stats adjustments 7 · easy

Triangles and slope reductionNCEES · Applied Mathematics

Law of sines and cosines

asin A = bsin B = csin C · c² = a² + b² − 2ab cos C

Two sides and the included angle: cosines. Two angles and any side: sines.

Two sides and a non-included angle (SSA) is the ambiguous case: two triangles may fit.

Try itmath 12 · medium math 13 · medium math 14 · hard

Triangle area

A = ½ ab sin C · A = √(s(s−a)(s−b)(s−c)), s = a + b + c2

Slope to horizontal

H = S sin z = S cos α · V = S cos z = S sin α · H = √(S² − h²) ≈ S − h²2S

S: slope distance
z: zenith angle (0° straight up, 90° level)
α: vertical angle from horizontal
h: elevation difference between tape ends

Zenith and vertical angle swap sine and cosine. z = 88°30′ means a 1°30′ upward sight.

Try itmath 15 · medium math 16 · easy field data 16 · medium field data 22 · hard

Grade

grade % = riserun × 100 = 100 tan α · +2.40% rises 2.40 ft per 100 ft station

Try itmath 23 · easy

Traverse computationsNCEES · Survey Computations

Latitude and departure

Lat = L cos Az · Dep = L sin Az

Signs come from the quadrant: Az 150° gives Lat negative (south), Dep positive (east). Swapping sin and cos is the classic error.

Try itmath 19 · medium plane calcs 5 · easy

Linear misclosure and precision

e = √(ΣLat² + ΣDep²) · precision = 1 : perimetere

Root-sum-square, never the arithmetic sum. Georgia requires 1:10,000 urban/suburban, 1:5,000 rural.

Try itplane calcs 6 · hard stats adjustments 18 · medium ga law 1 · hard ga mts 14 · medium

Compass (Bowditch) rule

correction to Lat = −ΣLat × Lperimeter · same for Dep

Opposite sign to the misclosure, proportional to course length. Transit rule uses the course's own latitude or departure instead of length. Crandall holds the angles and adjusts distances only.

Try itplane calcs 7 · medium stats adjustments 17 · medium plane calcs 8 · medium

Forward computation (COGO)

N₂ = N₁ + L cos Az · E₂ = E₁ + L sin Az

Try itplane calcs 9 · medium

Inverse between coordinates

L = √(ΔN² + ΔE²) · Az = atan ΔEΔN , then add 180° if ΔN < 0, add 360° if the result is negative

Check the quadrant from the signs of ΔN and ΔE before trusting the calculator. 3-4-5 triangles show up constantly: ΔN −300, ΔE +400 is 500 ft at 126°52′.

Try itmath 20 · hard plane calcs 10 · hard

AreasNCEES · Survey Computations

Coordinate (shoelace) method

2A = Σ (Nᵢ × Eᵢ₊₁ − Nᵢ₊₁ × Eᵢ), repeating the first point at the end

Divide by 2. Forgetting it doubles the acreage, and that is always one of the choices.

Try itmath 21 · medium plane calcs 12 · medium

Double meridian distance

DMD₁ = Dep₁ · DMDᵢ = DMDᵢ₋₁ + Depᵢ₋₁ + Depᵢ · 2A = Σ (DMDᵢ × Latᵢ)

The last DMD should equal minus the last departure; use it as a check.

Try itmath 22 · hard plane calcs 13 · medium

Trapezoidal rule (offsets)

A = d [ h₁ + hₙ2 + h₂ + h₃ + … + hₙ₋₁ ]

d: constant spacing between offsets

Try itmath 24 · medium plane calcs 14 · medium

Simpson's one-third rule

A = d3 [ (h₁ + hₙ) + 4 (h₂ + h₄ + …) + 2 (h₃ + h₅ + …) ]

Needs an odd number of offsets (even number of strips). Better for curved boundaries; trapezoidal for straight-ish ones.

Try itmath 25 · hard plane calcs 15 · medium

Horizontal curvesNCEES · Survey Computations

Degree of curve

arc definition: D = 5729.58R · chord definition: sin D2 = 50R

Highway work uses the arc definition (100 ft of arc). Railroads used the chord definition (100 ft chord).

Try itplane calcs 17 · easy

Curve parts

T = R tan Δ2 · L = 100 ΔD = R Δ π180 · LC = 2R sin Δ2 · E = R (sec Δ2 − 1) · M = R (1 − cos Δ2)

Δ: central (intersection) angle
T: tangent distance, PI to PC or PT
L: arc length PC to PT
LC: long chord
E: external, PI to curve midpoint
M: middle ordinate, chord midpoint to curve

Try itmath 17 · medium plane calcs 18 · medium plane calcs 19 · medium

Curve stationing

PC = PI − T · PT = PC + L · never PT = PI + T

Stationing runs along the arc, so PT comes from PC plus arc length. PI + T is the trap in every set.

Try itmath 18 · hard plane calcs 20 · hard

Deflection angles for layout

δ to a point at arc l from PC = lL × Δ2 = 1718.87 × lR minutes · chord = 2R sin δ

Total deflection from PC to PT is Δ/2. Deflection per 100 ft station equals D/2.

Try itplane calcs 21 · medium

Vertical curvesNCEES · Survey Computations

Elevation on an equal-tangent parabola

Elev(x) = Elev_BVC + g₁ x + (g₂ − g₁) x²2L · BVC = PVI − L2, EVC = PVI + L2

g₁, g₂: grades as decimals (ft/ft) if x and L are in feet, or in % if x and L are in stations
x: distance from BVC
L: curve length

Keep units consistent: percent grades with stations, or decimal grades with feet. Mixing them is the built-in trap.

Try itplane calcs 22 · medium plane calcs 23 · hard

High or low point

x = g₁ Lg₁ − g₂ = K |g₁| · K = LA, A = |g₂ − g₁| in %

Valid only if 0 ≤ x ≤ L. Otherwise the extreme is at an end of the curve.

Try itplane calcs 24 · hard

External distance (PVI to curve)

E = A L800 with A in % and L in ft · offset at x: y = A x²200 L

Crest curves sit below the PVI, sag curves above it.

Try itplane calcs 25 · medium

LevelingNCEES · Surveying Processes

Differential leveling

HI = Elev_BM + BS · Elev_TP = HI − FS · page check: ΣBS − ΣFS = Elev_end − Elev_start

Try itfield data 1 · easy field data 2 · easy

Curvature and refraction

c&r = 0.0206 F² ft (F in thousands of ft) · = 0.0675 K² m (K in km) · curvature alone 0.0239 F²

Rod readings are too high by c&r, so subtract it. Balanced BS and FS distances cancel it, which is the whole point of balancing sights.

Try itfield data 9 · medium field data 22 · hard

FGCS section misclosure

limit (mm) = C √D_km · C: 1st I 3 · 1st II 4 · 2nd I 6 · 2nd II 8 · 3rd 12

Try itfield data 10 · medium stats adjustments 25 · hard

Three-wire leveling and stadia

reading = U + M + L3 · distance = 100 (U − L) · check: U − M = M − L

Try itfield data 11 · medium

Peg test and bubble sensitivity

midway setup gives the true Δelev; near-end setup reveals collimation error · error = D × (sensitivity″ × 4.848 × 10⁻⁶)

Try itfield data 12 · medium field data 24 · hard

Trigonometric leveling

Δelev = S cos z + hi − hr + c&r · H = S sin z

hi: instrument height above station
hr: reflector height

Try itfield data 22 · hard

Weights in leveling

w ∝ 1L (line length) · weighted mean = Σ w xΣ w

Try itstats adjustments 13 · medium

Taping and EDMNCEES · Surveying Processes

Temperature correction

C_t = 0.00000645 (T − 68°F) L ft · C_t = 0.0000116 (T − 20°C) L m

Hot tape reads short, so the correction is positive (add it) when measuring an unknown distance. Reverse the sign when laying out a known distance.

Try itfield data 14 · medium stats adjustments 19 · medium

Pull (tension) correction

C_p = (P − P₀) LA E

P₀: standard pull
A: tape cross-section area
E: modulus of elasticity, about 29,000,000 psi for steel

Sag correction

C_s = − W² L24 P² = − w² L³24 P²

W: total weight of the suspended span
w: weight per unit length
P: applied pull

Always negative: sag makes the tape read long. Square the weight, and remember it is per suspended span.

Try itfield data 15 · medium field data 17 · medium

Normal tension

P_n = 0.204 W √(A E)√(P_n − P₀) , solved by iteration

The pull at which elongation exactly cancels sag, so a suspended tape reads its standardized length.

Try itfield data 23 · hard

EDM accuracy and atmosphere

σ = √(a² + (b × 10⁻⁶ × D)²) for ±(a mm + b ppm) · ≈ 1 ppm per 1°C, ≈ 10 ppm per 1 in Hg · 1 ppm = 1 mm per km

Constant and proportional parts add in quadrature, not arithmetically.

Try itstats adjustments 16 · medium field data 18 · medium

Prism (system) constant

K = AC − (AB + BC), measured on one line with three points

Try itfield data 19 · medium

Errors and statisticsNCEES · Applied Mathematics

Mean, residuals, standard deviation

x̄ = Σxn · v = x̄ − x · s = √ Σv²n − 1 · s_x̄ = s√n

Divide by n − 1 (Bessel). Dividing by n is always offered as a distractor.

Try itstats adjustments 4 · easy stats adjustments 5 · easy stats adjustments 9 · medium

Confidence multipliers

E₅₀ = 0.6745σ · E₉₀ = 1.6449σ · E₉₅ = 1.9599σ · ±1σ 68.27%, ±2σ 95.45%, ±3σ 99.73%

95% is 1.96σ, not 2σ. Small samples use Student's t with n − 1 degrees of freedom instead of z.

Try itstats adjustments 6 · easy stats adjustments 10 · medium stats adjustments 11 · medium

Error propagation

sum: σ = √(σ₁² + σ₂² + …) · n equal parts: σ = σ₁ √n · area a × b: σ_A = √((b σ_a)² + (a σ_b)²)

Random errors grow with √n; systematic errors grow with n. A level line of 16 setups has 4× the setup error, not 16×.

Try itstats adjustments 14 · medium stats adjustments 15 · medium

Blunders, systematic, random

blunders: detect and remove · systematic: model and correct (same sign, cumulative) · random: adjust (normal distribution)

Precision is repeatability; accuracy is closeness to truth. A wrong prism constant gives precise, inaccurate distances.

Try itstats adjustments 1 · easy stats adjustments 2 · easy stats adjustments 3 · easy

Weights, least squares, accuracy standardsNCEES · Applied Mathematics

Weights

w ∝ 1σ² · leveling: w ∝ 1L · angles: w ∝ n (repetitions) · weighted mean = Σ w xΣ w

Half the standard deviation means four times the weight, not twice.

Try itstats adjustments 12 · medium stats adjustments 13 · medium

Least squares

minimize Σ w v² = vᵀWv · r = n − u · σ̂₀² = vᵀWvr

n: observations
u: unknowns
r: redundancy (degrees of freedom)

σ̂₀² far above 1 means the observations are worse than their weights claim, or a blunder is present. Test with χ² on r degrees of freedom.

Try itstats adjustments 8 · easy stats adjustments 21 · hard

Error ellipses

standard ellipse ≈ 39.4% · 95% semi-axis = σ × √(2 F_{0.95; 2, r}) → 2.447 for large r, 4.37 for r = 3

Try itstats adjustments 22 · hard stats adjustments 23 · hard

NSSDA and ASPRS accuracy

RMSE_r = √(RMSE_x² + RMSE_y²) · Accuracy_r = 1.7308 RMSE_r = 2.4477 RMSE_x (if x = y) · Accuracy_z = 1.9600 RMSE_z

ASPRS 2014: NVA = 1.96 RMSE_z in open terrain; VVA = 3.0 RMSE_z (95th percentile) in vegetation. Use 20 or more well-distributed checkpoints.

Try itstats adjustments 24 · hard gis lis 17 · medium gis lis 22 · hard photo remote 16 · medium

ALTA/NSPS relative positional precision

RPP ≤ 2 cm (0.07 ft) + 50 ppm × D, at 95% confidence

D: direct distance between the two monuments

Try itstats adjustments 20 · medium boundary law 23 · hard

GNSSNCEES · Surveying Processes

GPS frequencies

f₀ = 10.23 MHz · L1 = 154 f₀ = 1575.42 MHz (λ ≈ 19.0 cm) · L2 = 120 f₀ = 1227.60 MHz (λ ≈ 24.4 cm) · L5 = 115 f₀ = 1176.45 MHz · λ = cf

Try itgnss 9 · medium gnss 10 · medium

Code chip lengths

chip = cchipping rate · C/A 1.023 Mcps → 293 m · P 10.23 Mcps → 29.3 m · 1 ns of timing ≈ 0.3 m of range

Try itgnss 11 · medium gnss 12 · medium

Dilution of precision

PDOP² = HDOP² + VDOP² · GDOP² = PDOP² + TDOP² · σ_position ≈ DOP × σ_range

VDOP is almost always larger than HDOP because there are no satellites below the horizon.

Try itgnss 6 · easy gnss 21 · hard

GNSS heights

h = H + N · H = h − N

h: ellipsoid height (what GNSS measures)
H: orthometric height (NAVD 88 elevation)
N: geoid height, negative across CONUS (about −8 to −53 m)

In CONUS N is negative, so H is larger than h everywhere.

Try itgnss 20 · medium geodesy datums 1 · easy geodesy datums 13 · medium

Antenna slant height

vertical height = √(slant² − r²) then add the ARP-to-phase-center offset

r: antenna radius to the measuring edge

Try itgnss 23 · hard

Differencing

single: 2 receivers, removes satellite clock · double: + 2 satellites, removes receiver clock · triple: + 2 epochs, removes ambiguities (finds cycle slips)

Try itgnss 15 · medium gnss 16 · medium

Geodesy and State PlaneNCEES · Surveying Principles

GRS80 ellipsoid

a = 6,378,137 m · 1/f = 298.257222101 · b = a (1 − f) = 6,356,752.314 m · e² = 2f − f² = 0.00669438

WGS84 shares a; its 1/f differs in the sixth decimal. The metre-level NAD 83 vs WGS 84 difference comes from the datum, not the ellipsoid.

Try itgeodesy datums 2 · easy geodesy datums 20 · medium geodesy datums 25 · hard

Elevation, scale, and combined factors

EF = RR + h , R = 20,906,000 ft (6,372,000 m) · CF = k × EF · grid = ground × CF

h: ellipsoid height (use H + N, not the elevation)
k: grid scale factor at the point

Even with k slightly above 1, CF is usually below 1 at any real elevation: grid distances are shorter than ground.

Try itgeodesy datums 9 · medium geodesy datums 10 · medium geodesy datums 22 · hard

Convergence and grid azimuth

γ ≈ Δλ sin φ · grid Az = geodetic Az − γ (east of the central meridian γ is positive)

Try itgeodesy datums 11 · medium geodesy datums 12 · medium

UTM

k₀ = 0.9996 · zones 6° wide, numbered from 180°W · central meridian = 6Z − 183 · FE 500,000 m, FN 0 (north) or 10,000,000 m (south)

Try itgeodesy datums 6 · easy gis lis 25 · hard

Georgia State Plane

East and West zones, transverse Mercator · k₀ = 0.9999 (1:10,000) · FE East 200,000 m, West 700,000 m · international foot since 1 July 2022

Lambert zones are for east-west states; transverse Mercator for north-south ones like Georgia. Do not confuse k₀ = 0.9999 with UTM's 0.9996.

Try itgeodesy datums 8 · easy ga law 9 · easy ga law 10 · medium ga law 11 · hard

Datum timeline

NAD 83(1986) → HARN → CORS96 → NSRS2007 → 2011 · NGVD 29 → NAVD 88 → NAPGD2022 · NATRF2022 = ITRF2020 at epoch 2020.0, plate-fixed

Try itgeodesy datums 21 · hard geodesy datums 14 · medium geodesy datums 19 · medium

Photogrammetry and remote sensingNCEES · Mapping Processes

Photo scale

S = fH − h = 1 : X · ground coverage G = X × format

f: focal length
H: flying height above datum
h: average ground elevation

Keep f and H − h in the same units. A 6 in lens at 6,000 ft above ground is 1:12,000. Engineer's scale 1 in = 500 ft is 1:6,000.

Try itphoto remote 1 · easy photo remote 2 · easy photo remote 9 · medium

Relief displacement

d = r hH · h = d Hr

r: radial distance from principal point to the image of the top
d: displacement between top and base images
H: flying height above the base of the object

Displacement is radial from the principal point on a truly vertical photo, from the nadir on a tilted one.

Try itphoto remote 10 · medium photo remote 24 · hard

Stereo parallax

h_A = H − B fp_A · Δh = H Δpp + Δp

B: air base (distance between exposures)
p: parallax of the point

Try itphoto remote 12 · medium photo remote 21 · hard

Flight planning

B = G (1 − end lap) · W = G (1 − side lap) · photos per line = lengthB + 1 · standard 60% end lap, 30% side lap

Try itphoto remote 7 · easy photo remote 13 · medium photo remote 14 · medium

Ground sample distance and C-factor

GSD = pixel × (H − h)f · H′ = C × contour interval

Lower flying height means smaller GSD and more detail. C-factors run about 1,200 to 2,500 by system.

Try itphoto remote 11 · medium photo remote 15 · medium

Lidar and NDVI

range = c t2 · NDVI = NIR − RedNIR + Red (−1 to +1, high means healthy vegetation)

Try itphoto remote 3 · easy photo remote 4 · easy

Map accuracy and GISNCEES · Mapping Processes

Map scale

ground = map distance × scale denominator · at 1:24,000, 1 in = 2,000 ft · larger scale = smaller denominator = more detail

Try itgis lis 8 · easy gis lis 9 · medium

National Map Accuracy Standards (1947)

horizontal: 90% of tested points within 130 in (scales larger than 1:20,000) or 150 in (1:20,000 and smaller) · vertical: 90% within ½ the contour interval

1:24,000 is smaller than 1:20,000, so 1/50 in applies: 40 ft.

Try itgis lis 16 · medium gis lis 21 · hard photo remote 25 · hard

Georeferencing

2D affine: 6 parameters (scale x, scale y, rotation, skew, 2 shifts) → at least 3 control points · conformal: 4 parameters → 2 points

Try itgis lis 19 · medium

Raster resolution

cells per side = extentcell size · halving the cell size quadruples the cell count

Try itgis lis 9 · medium gis lis 7 · easy

Public Land Survey SystemNCEES · Boundary Law

Township geometry

township = 6 mi square = 36 sections · section = 1 mi = 80 chains square = 640 acres · numbering starts NE, snakes west then east (boustrophedon)

Section 36 is the SE corner; south of it is Section 1 of the next township.

Try itplss 3 · easy plss 10 · medium

Aliquot parts

acres = 640product of the denominators · read smallest part first: NE¼ SW¼ SE¼ = 10 acres

Try itplss 4 · easy plss 9 · medium

Framework spacing

standard parallels every 24 mi north and south · guide meridians every 24 mi east and west · closing corners on the parallel’s south side

Try itplss 14 · medium plss 15 · medium

Convergence of meridians

c (ft) ≈ 43 × l × d × tan φ, with l and d in miles

Roughly 40 ft across a 6 mi township at latitude 40°. Excess or deficiency is thrown into the north and west tiers.

Try itplss 21 · hard plss 22 · hard

Single and double proportion

single: restored distance = record × measured overallrecord overall · double: proportion latitude N–S and departure E–W independently, then intersect

Single proportion for corners controlled in one direction (quarter corners, township-line corners). Double for corners common to four sections or four townships. Obliterated corners are restored from evidence, not proportioned.

Try itplss 23 · hard plss 24 · hard boundary law 22 · hard boundary law 24 · hard

Subdivision proration

corrected lot = record lot × measured blockrecord block

Prorate within the block between found original monuments. Never carry excess or deficiency across a street.

Try itboundary law 13 · medium boundary law 14 · medium

Business and licensure mathNCEES · Business Concepts

Continuing education conversions

1 CEU = 10 PDH · 1 contact hour = 1 PDH · peer-reviewed paper = 10 PDH · society office = 2 PDH per organization

Georgia: 7.5 PDH per annual renewal, carry forward at most 3.75.

Try itbusiness professional 21 · hard ga licensure 22 · hard

Break-even rate and multiplier

rate = direct labor + overheadbillable hours · multiplier = labor + overhead + profitdirect labor

Try itbusiness professional 22 · hard

PERT and critical path

t_e = a + 4m + b6 · σ = b − a6 · float = LS − ES = LF − EF; critical path has zero float

The simple average (a + m + b)/3 is the distractor.

Try itbusiness professional 23 · hard business professional 24 · hard

Georgia minimum technical standards (Rule 180-7)

Traverse closure, 180-7-.03

urban and suburban ≥ 1:10,000 · rural ≥ 1:5,000 · positional tolerance 0.1 ft urban, 0.25 ft suburban, 0.50 ft rural

Compass retracement of an old compass survey is allowed, but the work must still be reduced to a traverse meeting the closure standard.

Try itga law 4 · easy ga law 3 · medium ga mts 3 · easy ga mts 9 · medium

Leveling and contours, 180-7-.04

precise circuit: e ≤ 0.02 √M ft, never more than 0.05 ft · local benchmark circuit: e ≤ 0.1 √M ft · contours: at most 10% of the area in error by more than ½ the interval

M: circuit length in miles

Apply the formula, then the 0.05 ft cap. Nine miles gives 0.06 by formula, so 0.05 governs.

Try itga law 6 · hard ga law 7 · medium ga law 8 · medium ga mts 12 · medium ga mts 16 · medium

Monuments, 180-7-.05

durable, ferrous, at least 18 in long · ordinary: rod ≥ 0.2 in² or 3 in × 3 in concrete · land lot, district, county corners: 5/8 in rod, 1 in pipe, or 4 in square concrete or stone

Try itga mts 4 · easy ga mts 20 · medium

Plats and records, 180-7-.07

statement: “accurate within one foot in ____ feet”, filled from the actual computed map closure · field closure stated separately from map closure · retain plat and work materials 6 years from the latest date on it

Try itga law 2 · medium ga mts 6 · easy ga mts 19 · medium

GPS disclosures, 180-7-.09

state what portion used GPS, the equipment, the survey type (static, RTK, network RTK), and the precision as relative positional accuracy

Try itga mts 18 · medium

Sources are the ones cited on each linked question. Standards figures: FGCS 1984, ASPRS 2014, NSSDA, NMAS 1947, ALTA/NSPS 2021, Georgia Board Rule 180-7.