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Road Horizontal Curve Calculator

Calculate horizontal curve geometry for road design including radius, deflection angle, tangent length, chord length, and sight distance.

Highway & Transportation Highway engineers, transportation planners Commercial Intent: HIGH

Engineering Formulas

Horizontal Curve Geometry

T = R × tan(Δ/2)
L = R × Δrad
C = 2R × sin(Δ/2)
M = R × (1 - cos(Δ/2))
E = R × (1/cos(Δ/2) - 1)

T: Tangent length (m)

L: Curve length along arc (m)

C: Chord length (m)

M: Mid-ordinate (m)

E: External distance (m)

R: Curve radius (m)

Δ: Deflection angle (degrees)

Superelevation

e = V² / (g × R) - f
V in m/s, g = 9.81 m/s²

e: Superelevation rate (m/m)

V: Design speed (m/s)

f: Lateral friction factor (≈0.15)

Stopping Sight Distance (SSD)

SSD = V × t + V² / (2g(f ± G))

SSD: Stopping sight distance (m)

t: Reaction time (≈2.5s)

G: Grade (%)

Worked Example

Rural Highway Curve Design

radius: 300delta: 45designSpeed: 80

Tangent

T = 300 × tan(45/2) = 300 × 0.414 = 124.26 m

Curve

L = 300 × 0.785 = 235.62 m

Chord

C = 2 × 300 × sin(22.5) = 229.56 m

SuperE

e = 22.22²/(9.81×300) - 0.15 = 0.018 (1.8%)

SSD

SSD = 22.22 × 2.5 + 22.22²/(2×9.81×0.35) = 127.4 m

Result: R=300m, Δ=45° → T=124.3m, L=235.6m, e=1.8%, SSD=127m

Engineering Notes

All curves should be checked for stopping sight distance — the curve should be visible for at least the SSD length.

For compound curves (two radii), the ratio of radii should not exceed 1.5:1 for driver comfort.

Superelevation should be developed gradually over the spiral or tangent runout (typically 1:200 slope transition).

Consider trucks and buses for off-tracking — wider lanes may be needed on sharp curves.

Night visibility: ensure curve delineation with retroreflective markers on the outside of curves.

Assumptions

• Circular curve (no spiral transition)

• Level grade for sight distance calculation

• Maximum superelevation: 7%

• Lateral friction factor: 0.15

Common Mistakes

✕ Using degrees instead of radians in curve length formula

✕ Applying superelevation formula with km/h instead of m/s

✕ Forgetting to convert design speed from km/h to m/s (÷ 3.6)

✕ Not checking that SSD is less than curve length for safety

✕ Designing curves without considering vehicle off-tracking

Frequently Asked Questions

What is the minimum radius for a highway?

For design speed 100 km/h with 7% superelevation, minimum radius ≈ 400m. For 80 km/h: ≈ 250m. For 50 km/h: ≈ 100m. Lower speeds allow tighter curves.

What is superelevation and why is it needed?

Superelevation is the banking of a road curve, tilting the roadway toward the inside. It counteracts centrifugal force, allowing vehicles to navigate curves safely at design speed.

What is the maximum superelevation rate?

Typical maximum superelevation: 7% for highways with snow/ice, 10% for warm climates. Urban roads: 4–6%. The absolute maximum is 12% per AASHTO guidelines.

How is stopping sight distance calculated?

SSD = reaction distance + braking distance. Reaction distance = V × t (t = 2.5s typical). Braking distance depends on speed, friction, and grade. Total SSD is used to check curve safety.

What is the degree of curve?

The degree of curve (D) is the central angle subtended by a 100m chord. D ≈ 5729.58 / R for flat curves (arc definition). It is an alternative measure of sharpness used in highway surveying.

What is the difference between tangent length and curve length?

Tangent length (T) is the distance from the point of intersection (PI) to the point of curvature (PC) or point of tangency (PT). Curve length (L) is the actual arc length along the curve.

When should a spiral transition curve be used?

Spiral transitions should be used for design speeds above 60 km/h or when superelevation runoff cannot be accommodated within the simple curve. Spirals provide gradual steering input.

What is the minimum curve length?

Minimum curve length for driver comfort: L_min = V × 2s (2 seconds of travel). For V=80 km/h: L_min ≈ 45m. AASHTO recommends absolute minimum of 30m for all curves.