# Vertical Curve Calculator

URL: https://speedycalculator.com/calculators/construction/vertical-curve/
Last updated: 2026-10-25

> The vertical curve calculator designs a symmetric parabolic vertical curve for roads and pipelines: BVC and EVC stations and elevations, the elevation at any station, the high or low point, and the K value.

## Inputs

- Incoming grade g₁ (%)
- Outgoing grade g₂ (%)
- Curve length (ft, m, in, yd, cm)
- PVI station (ft, m, in, yd, cm)
- PVI elevation (ft, m, in, yd, cm)
- Station of interest (ft, m, in, yd, cm)

## Results

- BVC station
- BVC elevation
- EVC station
- EVC elevation
- Elevation at station of interest
- High / low point station
- High / low point elevation
- K value (length per % grade change)

## Formula

```
E(x) = E_BVC + g₁ x + (g₂ − g₁) x² ÷ 2L
BVC = PVI − L/2, E_BVC = E_PVI − g₁ L/2; EVC = PVI + L/2, E_EVC = E_PVI + g₂ L/2
High/low point x = −g₁ L ÷ (g₂ − g₁); K = L ÷ |g₂ − g₁| (g in %)
```

## Explanation

Where two road grades meet, a parabolic vertical curve provides a smooth transition. Crest curves (g₁ > g₂) limit sight distance; sag curves (g₁ < g₂) affect headlight reach and drainage. Designers choose the curve length from the K value – length per percent change of grade – recommended for the design speed.

### How to use the Vertical Curve Calculator

- **Incoming grade g₁**
- **Outgoing grade g₂**
- **Curve length**
- **PVI station**
- **PVI elevation**
- **Station of interest**

Results update as you type, and every field accepts the units shown in its menu.

### How it works

Enter the incoming and outgoing grades in percent, the curve length, the station and elevation of the point of vertical intersection (PVI) and a station where you want the elevation.

### Tips for an accurate estimate

- Measure angles with a digital angle finder or sliding bevel, not by eye.
- Make a test cut in scrap before cutting expensive stock.
- Small angle errors add up over many joints – check the first assembly before cutting the rest.
- Keep a written list of the dimensions and angles you set on the saw or machine.

### Common mistakes to avoid

- Reading the saw scale as the angle from the edge rather than from square.
- Rounding intermediate results too early.
- Mixing degrees and percent grade.

### Inputs explained

FieldWhat to enterIncoming grade g₁In %Outgoing grade g₂In %Curve lengthUnits: ft, m, in, yd, cmPVI stationUnits: ft, m, in, yd, cmPVI elevationUnits: ft, m, in, yd, cmStation of interestUnits: ft, m, in, yd, cm

### What each result means

- **BVC station** = [PVI station] - [Curve length]÷2
- **BVC elevation** = [PVI elevation] - [Incoming grade g₁]÷100×[Curve length]÷2
- **EVC station** = [PVI station] + [Curve length]÷2
- **EVC elevation** = [PVI elevation] + [Outgoing grade g₂]÷100×[Curve length]÷2
- **High / low point elevation** = [BVC elevation] + [Incoming grade g₁]÷100×([High ÷ low point station] - [BVC station]) + ([Outgoing grade g₂] - [Incoming grade g₁])÷100×([High ÷ low point station] - [BVC station])^2÷(2×[Curve length])
- **K value (length per % grade change)** = [Curve length]÷abs([Outgoing grade g₂] - [Incoming grade g₁])

### Example values

How the main result changes when **Incoming grade g₁** changes and everything else stays at the example values above:

Incoming grade g₁ (%)Elevation at station of interest (ft)1.5497.3332.25496.3333495.3333.75494.3334.5493.3336491.333

## Worked example

Inputs — Incoming grade g₁: 3 %; Outgoing grade g₂: -2 %; Curve length: 600 ft; PVI station: 1,500 ft; PVI elevation: 500 ft; Station of interest: 1,400 ft.

Results — BVC station = 1,200 ft; BVC elevation = 491 ft; EVC station = 1,800 ft; EVC elevation = 494 ft; **Elevation at station of interest = 495.333 ft**; High / low point station = 1,560 ft; High / low point elevation = 496.4 ft; K value (length per % grade change) = 120 ft.

## Key terms

- **PVI**: Point of vertical intersection of the two tangent grades.
- **BVC / EVC**: Beginning and end of the vertical curve.

## FAQ

**What is a vertical curve?**
A parabola that joins two straight grades so the rate of change of grade is constant.

**What is the K value?**
The horizontal length needed for a 1% change in grade; AASHTO tables give minimum K for crest and sag curves by design speed.

**Where is the high point of a crest curve?**
At x = g₁L ÷ (g₁ − g₂) from the BVC, if it falls within the curve.

**What formula does the Vertical Curve Calculator use?**
E(x) = E_BVC + g₁ x + (g₂ − g₁) x² ÷ 2L.


## Sources

- [AASHTO – A Policy on Geometric Design of Highways and Streets](https://www.transportation.org/)