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Enter two projected grid coordinates to calculate t-T at both ends of the line.
t-T Correction Visual
The t-T correction is the small angle between the tangent to a projected geodetic arc and the straight grid chord between two plotted coordinates.
What Is the t-T Correction?
The t-T correction, often called the arc-to-chord correction, is a small angular correction used in precise surveying when a geodetic line is represented on a projected grid. A geodetic line projects as a slight curve on a Transverse Mercator grid, while most coordinate computations connect the two plotted endpoints with a straight chord. The t-T correction accounts for the angle between the tangent to that projected arc and the straight grid chord.
For short site lines the correction may round to zero. For longer control lines, national-grid work, or high-order bearing reductions, a few seconds of arc can matter. This calculator gives a transparent estimate from the two grid coordinates, false origin, and a mean radius value.
Arc-to-Chord Correction Formula
The calculator uses the standard small-angle Transverse Mercator approximation:
tT_A = dE(2N_A + N_B) / 6R² tT_B = dE(N_A + 2N_B) / 6R²Here, dE is the easting difference from Point A to Point B, N_A and N_B are northings measured relative to the projection false origin, and R is the selected mean radius. The result is first computed in radians and then converted to seconds of arc. The false origin is important because raw grid northings can give the wrong magnitude or sign when the formula expects relative northings.
When Surveyors Use t-T
Surveyors use t-T when converting between geodetic azimuths and grid bearings on projected coordinate systems. It is most relevant on long control lines, triangulation or traverse reductions, and workflows where a field-observed or geodetically computed azimuth must be reconciled with CAD, GIS, or national-grid bearings. It is not usually needed for small construction offsets or everyday short-distance layout.
t-T vs Grid Convergence
Grid convergence and t-T are different corrections. Grid convergence is the angle between true north and grid north at a point. t-T is the angle between the tangent to the projected geodetic arc and the straight grid chord between two coordinates. A full bearing reduction may need both: first account for convergence, then account for the arc-to-chord correction at the relevant endpoint.
How to Choose the Projection Model
The OSGB preset uses a practical false origin and radius for British National Grid-style calculations. The UTM preset uses the common 500,000 m false easting and a generic Earth-radius approximation. Custom mode lets you enter agency-specific constants for another Transverse Mercator grid. If your survey authority publishes a specific radius product, false origin, or reduction workflow, use those values instead of the generic defaults.
Limits of This Approximation
This tool is an engineering calculator, not a replacement for official geodetic software. The approximation is useful for education, checks, and many practical survey notes, but legal boundary work and statutory national-grid transformations should follow the governing agency procedure. The result is also sensitive to coordinate system choice, false northing, and unit consistency. If the calculator shows a large warning, verify the line in a full geodetic package.
Related Surveying Calculators
- Grid Convergence Calculator for true north to grid north angle checks.
- UTM Zone Finder for identifying zone and central meridian.
- WGS84 to UTM Converter for projected easting and northing.
- UTM to Lat/Long Converter for reverse coordinate conversion.
- Distance & Bearing Calculator for coordinate-pair distance and bearing checks.
- Azimuth Calculator for geodetic azimuth between coordinates.
- COGO Point Calculator for coordinate layout by bearing and distance.
Frequently Asked Questions
Is t-T the same as grid convergence?
No. Grid convergence compares true north and grid north. t-T compares a projected arc tangent and the straight grid chord between two points.
Why are there two t-T values?
The tangent to the projected arc at Point A is not parallel to the tangent at Point B. Long survey lines therefore have an endpoint correction at each end.
Can I use latitude and longitude?
No. This calculator expects projected easting and northing coordinates in a Transverse Mercator-style grid. Convert geographic coordinates to the relevant projected CRS first.
Is this suitable for legal boundary work?
Use official agency software, published procedures, and a qualified surveyor for legal boundary or statutory national-grid reductions. This web calculator is designed for transparent checks and education.