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Common Surveying Formulas

• Area of a Triangle: (1/2) * base * height
• Slope Distance: √(Horizontal Distance² + Elevation Difference²)
• Horizontal Distance: Slope Distance * cos(Slope Angle)
• Azimuth to Bearing: Azimuth - 180° (if Azimuth > 180°)
• Area of a Circular Sector: (π * radius² * angle) / 360
• Chord Length: 2 * radius * sin(angle / 2)
• Latitude (ΔY): Distance * cos(Azimuth)
• Departure (ΔX): Distance * sin(Azimuth)
• Ellipsoid Arc Length: (ΔLongitude * cos(Latitude)) * 111.32
• Volume of a Prismoidal Solid: (h/3) * (A1 + 4Am + A2)
• Deflection Angle: tan⁻¹(Offset Distance / Distance from Station)
• Radius of Curve: (Chord Length / 2) / sin(Central Angle / 2)
• Intersection Point (IP) of Two Lines: (m1x1 + m2x2) / (m1 + m2)
• Inverse Slope Angle: tan⁻¹((Elevation Difference) / (Horizontal Distance))
• GPS Baseline Adjustment: √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)