Field guide
From an instrument sight to a useful ground-level result
Check the source, calculation convention, exceptions and output before continuing your workflow.
Choose the distance you actually measured
A slope distance to horizontal distance calculation is useful when a field export still contains instrument-to-target sight lengths. A coordinate calculation or setting-out schedule may need horizontal distances instead. Start by checking the export definition: a column named distance could already contain a reduced horizontal value. Applying another trigonometric reduction would shorten it incorrectly, even though the spreadsheet would still look plausible.
This calculator separates three outputs: horizontal distance, the vertical component of the sight line, and the elevation difference between the ground points. An optional station elevation produces a target ground elevation. It does not derive a horizontal direction or new Easting and Northing from a vertical angle.
Prepare a traceable observation table
Upload CSV, TXT, TSV or XLSX, or paste a small table. The default layout is point identifier, slope distance, angle, instrument height, target height, station elevation and description. Column numbers start at one. Map zero only for an absent identifier, station elevation or description; the other four measurements are required. Different mapped meanings must use different columns.
For a workbook, choose its worksheet before calculating. Keep point names as text when leading zeros matter. Formula cells need to be converted to checked values in the source workbook. Additional source fields and the complete original text remain in the JSON report, so a reviewer can trace a result beyond the concise export columns.
Distinguish a zenith angle from an elevation angle
A zenith angle is measured from upward vertical: zero points upward, ninety degrees is horizontal and one hundred eighty degrees points downward. The supported range is zero through one hundred eighty degrees. A signed vertical or elevation angle is measured from horizontal: positive values look upward and negative values downward, within minus ninety through plus ninety degrees.
Select the definition explicitly. A value near ninety degrees could be a nearly horizontal zenith sight but a nearly vertical elevation sight. The tool does not decide which interpretation looks more reasonable. Raw face-two circle readings are rejected outside the supported range; normalize and review face observations in the source surveying software first.
Select an angle notation instead of guessing
Decimal degrees, separated degrees minutes seconds, compact dd.mmss and gon are separate choices. For example, 89.4050 in compact notation means eighty-nine degrees, forty minutes and fifty seconds. In decimal-degree mode the same string means 89.405 degrees. These are different directions, and both can look valid without an explicit format choice.
For separated DMS, use three components such as 89 40 50 or degree, prime and double-prime symbols. Minutes and seconds must be below sixty. The sign belongs to the entire vertical angle, including a negative angle smaller than one degree. A hundred gon represents a right angle. Decimal numbers use a period; choose a semicolon delimiter when your table requires it.
Understand the geometric reduction
For zenith angle Z and slope length S, horizontal distance is S multiplied by sin Z and the sight-line vertical component is S multiplied by cos Z. With a signed elevation angle v, the equivalent expressions are S multiplied by cos v and S multiplied by sin v. The horizontal result is nonnegative within the supported angle ranges.
The implementation treats exact horizontal and vertical sights explicitly, avoiding tiny trigonometric remnants at cardinal angles. This convenience does not improve the field observation accuracy. All displayed calculated values use six decimal places; downloads retain the underlying numerical result. Choose downstream rounding according to your measurement and deliverable requirements, not the number of digits shown here.
Apply instrument and target heights once
The ground-level elevation difference equals the sight-line vertical component plus instrument height minus target height. Heights must be vertical distances to the relevant instrument and target centers. A sloping tape measurement to a notch or another reference point is not automatically the required vertical height; follow your instrument's documented procedure before entering it.
A missing height is an error, rather than an assumed zero. Enter zero explicitly only when the physical setup justifies that value. Heights can vary between observations, so each record carries its own pair. Do not enter an already ground-reduced vertical difference as if it were a raw sight angle, or repeat a height correction previously applied by another program.
Reproduce the worked example
Load the example and select zenith angles in decimal degrees with all lengths in metres. A slope length of 100, a zenith angle of 60, an instrument height of 1.5 and a target height of 2 give a horizontal distance of approximately 86.602540 and a sight-line vertical component of 50. The ground-level difference is therefore 49.5.
If the station elevation is 100, the target ground elevation is 149.5. A second sight with the same distance and heights but a ninety-degree zenith angle has zero sight-line vertical component while the ground difference is minus 0.5. That distinction explains why a horizontal telescope sight does not necessarily connect two equal ground elevations.
Keep units and the height datum consistent
Select metres, international feet or US survey feet for every distance and height in the current batch. The choice labels the numbers; it does not convert one column from feet to metres. Mixing slope distance in metres with instrument height in feet produces an incorrect result even if the angle definition is right. Convert source values deliberately before combining them.
Station elevation is optional. Leaving it blank still allows a relative ground difference, while target elevation stays blank. If station elevation is supplied, its vertical datum is inherited by the result. This page does not transform ellipsoidal heights to orthometric elevations or establish a benchmark. Include the job reference, units and correction state in the report note.
Know which corrections remain outside this page
This is a plane geometric reduction, after you check the instrument's observation settings. It does not apply prism constants, atmospheric parts-per-million corrections, curvature and refraction, collimation, instrument tilt, face-pair averaging or network adjustment. Those operations have their own inputs and conventions. An apparently small difference from instrument software may reflect a different correction pipeline rather than rounding.
It also does not convert local horizontal ground distance into a projection grid distance. If that is required, use a documented combined factor with the separate ground-to-grid workflow. A distance that has already received an unknown correction should be traced back to its source before further processing. The confirmation checkbox records your review; it cannot discover the instrument settings from a CSV.
Review errors without losing observations
Positive slope distance and nonnegative instrument and target heights are required. Invalid numbers, missing required values, malformed rows and unsupported angles stay in their original order with an error and blank calculated fields. Repeated point identifiers remain separate observations. A zero-distance backsight placeholder, for example, should not silently become a successful three-dimensional observation.
The public regression dataset uses Carlson's SurvCE tutorial file recorded with a Leica TPS instrument. Its observations are extracted into CSV and XLSX with source line references, and valid results are compared with an independent Python calculation. This supports the file workflow and arithmetic; it is not a certification of a real project's coordinates or reproduction of Carlson's adjustment process.
Export a complete handoff
After reviewing the statuses, download CSV or XLSX with every source record, selected angle convention, unit and computed value. Invalid rows remain present. JSON includes the complete input and settings for a fuller audit. Computation runs on your device in a cancellable worker. The input limit is ten MiB and one hundred thousand observations, with an additional size guard on text exports.
For a later coordinate calculation, use the horizontal-distance column only after checking its ground or grid meaning. Supply the required azimuth and origin independently. A vertical angle alone cannot provide that direction. Preserve the original observation report alongside any coordinate output, so a later reviewer can distinguish measurement reduction from coordinate generation and subsequent adjustment.