Minimum Horizontal Curve Radius Calculator
Enter a design speed and pick a maximum superelevation rate — the tool computes the AASHTO minimum radius using the side-friction curve from the current Green Book (7th Edition, 2018), interpolated for any speed between 20 and 130 km/h.
Reference table
Formula & source
V = design speed (km/h), emax = maximum superelevation rate (decimal), fmax = maximum side-friction factor for that speed (open-roadway condition, AASHTO Method 5 distribution).
Source: AASHTO, A Policy on Geometric Design of Highways and Streets (Green Book), 7th Edition, 2018 — Tables 3-7/3-8/3-9/3-10, Minimum Radii for Design Superelevation Rates. fmax values used here (0.35 at 20 km/h down to 0.10 at 120–130 km/h) are interpolated from the published metric tables for emax = 4%, 6%, and 8%, cross-checked against each other for consistency.
This tool is for preliminary design and checking. Always confirm against the current edition of the Green Book (or the governing agency's design manual) before finalizing a design.
About this minimum curve radius calculator
This tool returns the smallest horizontal curve radius that may be used at a given design speed, following AASHTO geometric design practice. It is aimed at highway and road design engineers, transport planners and students setting out or checking a horizontal alignment. Pick the maximum superelevation rate your design standard allows, enter the design speed, and the calculator returns the minimum radius along with the side friction factor it used.
How the calculation works
The governing relationship is
Rmin = V² / [127 × (emax + fmax)],
where V is the design speed in km/h, emax is the maximum superelevation
rate as a decimal, and fmax is the maximum side friction factor for that
speed. The constant 127 converts speed in km/h into consistent units with
gravitational acceleration. Because fmax is not fixed, the calculator
interpolates it from the AASHTO breakpoints — roughly 0.35 at 20 km/h falling to
0.10 at 120–130 km/h — and reports the value used with every result.
Choosing the maximum superelevation rate
- 4% — where snow and ice occur, or in urban areas where vehicles may have to stop on the curve.
- 6% — widely used general practice for most conditions.
- 8% — rural highways in warm climates without snow and ice.
A higher emax permits a tighter curve at the same speed, so the choice has a direct effect on the alignment. Always follow the governing agency's design manual rather than picking the value that gives the smallest radius.
Why speed drives radius so strongly
Radius grows with the square of speed, so doubling the design speed roughly quadruples the required radius. The effect compounds because the permitted side friction factor also drops as speed rises, leaving less friction available to turn the vehicle. That is why high speed alignments need long, flat curves, and why raising a design speed late in a project can force a complete realignment.
Using the result
The value returned is a minimum, not a target. Designers normally adopt a radius comfortably above it so the curve is not operating at the limit of the assumed comfort criteria. If you enter a speed outside the verified 20–130 km/h range, the tool holds fmax at the nearest boundary value and flags the result as an approximation. Once the plan geometry is settled, the profile is designed with the vertical curve design calculator.
Frequently asked questions
How is the minimum horizontal curve radius calculated?
The minimum radius is the design speed squared divided by 127 times the sum of the
maximum superelevation rate and the maximum side friction factor, or
R = V² / [127 × (emax + fmax)]. V is
in kilometres per hour and emax is a decimal, so 6% is entered as 0.06.
The constant 127 comes from converting speed in km/h to metres per second and
dividing by gravitational acceleration.
What is superelevation and what does emax mean?
Superelevation is the banking of the roadway on a curve, tilting the surface inward so part of the centripetal force needed to turn the vehicle is provided by gravity rather than tyre friction alone. emax is the maximum superelevation rate the design standard permits, and it depends on climate and terrain. Four percent is typical where ice and snow occur or in urban areas with frequent stopping, six percent is common general practice, and eight percent suits rural highways in warm climates.
What is the side friction factor fmax?
The side friction factor is the lateral friction between tyre and pavement that a design assumes is available to help turn the vehicle. AASHTO sets it from driver comfort rather than the friction limit of the tyre, so it falls as speed rises, from about 0.35 at 20 km/h down to 0.10 at 120–130 km/h. This calculator interpolates fmax for the speed you enter and reports the value used.
Should I use 4%, 6% or 8% maximum superelevation?
It depends on the governing design manual and the conditions. Four percent is used where snow and ice are common or in urban areas where vehicles may stop on the curve, six percent is a widely used general value, and eight percent is used on rural highways in areas without snow and ice. Higher emax produces a smaller minimum radius for the same speed, so the choice directly affects how tight a curve is permitted.
Why does a higher design speed need a larger curve radius?
Radius increases with the square of speed, so doubling the design speed roughly quadruples the required radius. The effect is compounded because the permitted side friction factor also falls as speed rises, leaving less friction to help turn the vehicle. This is why high speed alignments need long, flat curves.
Can I use a curve radius smaller than the calculated minimum?
No. The calculated value is the smallest radius that can be used at that design speed with the chosen maximum superelevation while staying within the assumed comfort limits. Using a tighter curve means either exceeding the permitted superelevation, relying on more side friction than the standard allows, or reducing the design speed. In practice designers usually adopt a radius comfortably above the minimum.
Which AASHTO edition does this calculator use?
It uses the side friction values from A Policy on Geometric Design of Highways and Streets, the AASHTO Green Book, 7th Edition, 2018, from the minimum radii tables for design superelevation rates. The tool is intended for preliminary design and checking, and results should always be confirmed against the current edition or the governing agency design manual before a design is finalised.
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