Superelevation Calculator

Plan safe bends using speed, radius, and grip. Get bank rate, angle, runoff, and alerts. Export results as sheets or printouts for site teams

Calculator

Based on e + f = v² / (gR)
Typical range often ~0.08–0.18, by standard.
Use decimal slope; 0.08 = 8%.
Used for an advisory warning only.
Runoff = e × width, height diff across pavement.
Use 9.81 m/s² unless specified.

Example Data Table

Speed Radius f e (approx) e (%) Angle (deg)
60 km/h 200 m 0.12 0.03 3% 1.7°
80 km/h 250 m 0.12 0.09 9% 5.1°
100 km/h 350 m 0.10 0.11 11% 6.3°

Values are illustrative. Always verify with local design rules.

Formula Used

The core relationship for a vehicle on a horizontal curve is: e + f = v² / (gR)

  • e = superelevation rate (decimal; 0.08 = 8%).
  • f = side friction factor (dimensionless).
  • v = speed (m/s after unit conversion).
  • R = curve radius (m after unit conversion).
  • g = gravity (m/s²).

The banking angle is θ = arctan(e). The runoff height difference across pavement is Δh = e × width.

How to Use This Calculator

  1. Select what you want to solve: e, radius, speed, or friction.
  2. Enter the known values and pick matching units.
  3. Set an advisory maximum e limit for warnings.
  4. Press Calculate to view results above the form.
  5. Use Download CSV or Download PDF to export.

For best field use, keep units consistent and confirm curve radius measurement method.

Superelevation in Roadway Construction

1) Why curve banking matters

Superelevation is the cross-slope applied on a horizontal curve so part of the lateral demand is carried by gravity instead of tire side friction alone. By balancing forces, banking improves comfort, lowers skid risk, and helps keep heavy vehicles stable at design speed.

2) The key relationship

Designers commonly use the equilibrium form e + f = v²/(gR). Here e is the superelevation rate (decimal), f is side friction factor, v is speed, and R is curve radius. This calculator can solve for any one of these variables.

3) Typical ranges and limits

Many agencies cap e within about 4%–14%, depending on climate, urban constraints, and slow-moving traffic. Side friction assumptions often fall around 0.08–0.18 for design checks. Always apply your local standard, because permitted values vary by road class and environment.

4) Units and conversions

Field data may arrive as mph, km/h, meters, or feet. Internally, the calculation uses m/s and meters so results stay consistent. Conversions are handled automatically, but you should keep the input pairings logical, especially when comparing multiple curves across a corridor.

5) Runoff and height difference

Constructability is often governed by how the cross-slope transitions. A practical measure is runoff height difference across pavement: Δh = e × width. For example, with 8% on 7 m width, the height difference is 0.56 m. Use this to plan edging, drainage, and layer thickness control.

6) Checking safety warnings

When the computed e exceeds your selected advisory maximum, it suggests the curve may be too tight for the chosen speed under conservative friction. Solutions include lowering speed, increasing radius, or using a design approach that matches the governing guideline.

7) Choosing a design speed

Design speed should reflect expected operating speed, not just posted speed. Consistency along the alignment helps reduce surprises. If a curve requires extreme banking or friction, it may indicate a need for geometric revision or targeted speed management.

8) Using results on site

For construction teams, outputs like bank angle and runoff height difference support staking, paving control, and QA checks. Exporting results to CSV helps keep a curve-by-curve register, while PDF is useful for quick printing in the field. Always validate the final crossfall with surveying and compaction tolerances.

FAQs

1) What does “e” represent?

It is the superelevation rate, expressed as a decimal cross-slope. For example, 0.08 means an 8% crossfall from the inner to the outer edge on the curve.

2) Why is side friction included?

Friction accounts for tire-road grip that also resists lateral motion. In the design equation, banking and friction share the demand. Lower assumed friction generally increases required superelevation.

3) Can e be negative?

Yes, the math can yield a negative value if speed is low, radius is large, or friction input is high. In practice, you would review inputs or use normal cross-slope rather than negative banking.

4) What is the difference between e (%) and e (decimal)?

Decimal e is used in formulas (0.08). Percent e is the same value multiplied by 100 (8%). The calculator shows both for clarity and reporting.

5) How should I pick the max e check?

Select the limit used by your standard or project constraints. Urban drainage, ice, slow traffic, and heavy vehicles can justify lower caps. This tool flags exceedance as an advisory warning.

6) Does runoff equal superelevation length?

No. This calculator reports runoff height difference (Δh) across pavement width. Transition length depends on allowable slope change rates and project criteria, which vary by guideline.

7) Which mode should I use most often?

Use “Solve e” when speed, radius, and friction are known. Use “Solve speed” to estimate safe speed for an existing curve. Use “Solve radius” during geometric layout options.

Accurate curve banking helps crews build safer roads daily.

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