Calculator Form
Formula Used
Polar true position compares a designed point and a measured point generated from the same origin by angle and distance.
For North-based clockwise azimuth:
ΔE = D × sin(θ)
ΔN = D × cos(θ)
X = X₀ + ΔE
Y = Y₀ + ΔN
For East-based counterclockwise angle:
ΔX = D × cos(θ)
ΔY = D × sin(θ)
X = X₀ + ΔX
Y = Y₀ + ΔY
True position error:
TP = √[(Xmeasured − Xdesign)² + (Ymeasured − Ydesign)²]
The point passes when TP ≤ tolerance radius.
How to Use This Calculator
- Enter the point name for your field reference.
- Provide the origin coordinate values.
- Choose the angle unit that matches your survey data.
- Select the reference system used for the angle measurement.
- Enter the design angle and design distance.
- Enter the measured angle and measured distance.
- Type the allowable tolerance radius.
- Press the calculate button to view coordinates, offsets, true position, pass or fail status, CSV export, PDF export, and the Plotly graph.
Example Data Table
| Point | Origin X | Origin Y | Design Angle | Design Distance | Measured Angle | Measured Distance | Tolerance | True Position Error |
|---|---|---|---|---|---|---|---|---|
| P1 | 5000.000 | 10000.000 | 35.000° | 42.500 | 35.120° | 42.650 | 0.300 | 0.175 |
| P2 | 1250.000 | 880.000 | 120.000° | 18.200 | 119.930° | 18.160 | 0.150 | 0.045 |
| P3 | 300.000 | 450.000 | 275.500° | 56.800 | 275.950° | 56.620 | 0.250 | 0.462 |
FAQs
1. What is polar true position?
It is the radial error between a designed point and a measured point created from the same origin using angle and distance values.
2. Why is this useful in construction?
It helps verify layout accuracy for anchors, bolts, columns, utilities, and stakeout points before work progresses further on site.
3. Which reference system should I choose?
Choose North-based clockwise azimuth for common surveying practice. Choose East-based counterclockwise when your project uses mathematical polar angles.
4. What does the tolerance radius mean?
The tolerance radius is the maximum acceptable radial deviation from the designed point. Values above it fail the layout check.
5. Can I use degrees, gons, or radians?
Yes. The calculator converts the selected unit internally and keeps the displayed angle difference in the same unit you entered.
6. What do Delta X and Delta Y show?
They show the directional offset between measured and designed coordinates. Positive or negative signs indicate the correction direction.
7. Does the graph help field review?
Yes. The graph quickly shows where the measured point sits relative to the design point and the tolerance boundary.
8. Can I save the calculation output?
Yes. Use the CSV button for spreadsheet review and the PDF button for a portable report you can share.