Vertical Curve Calculator

Online statistics and data analysis support for USA, UK and international clients. No exams, no impersonation, no fabricated data.
United States calculator

Evaluate a parabolic vertical curve at a station

Enter entering and exiting grades, curve length, PVC elevation and distance from PVC.

vertical profile

Project inputs

Vertical Curve Calculator results

How this Vertical Curve Calculator works

A standard equal-tangent parabolic equation computes elevation and grade at the selected station.

Important: Design sight distance and drainage require applicable highway standards and engineering review.
What assumptions should I verify?

The Vertical Curve Calculator uses U.S.-first defaults where conventions affect Entering grade %, Exiting grade %, and Curve length ft; its visible selectors identify alternate measurements explicitly. The reported Elevation at station, Instantaneous grade, and Algebraic grade change follows the selected units and the same canonical equation Grade Change = abs((g2-g1) × 100).

Is information sent anywhere?

The Vertical Curve Calculator evaluates Grade Change = abs((g2-g1) × 100) locally in the browser. Values entered for Entering grade %, Exiting grade %, and Curve length ft are used to produce Elevation at station, Instantaneous grade, and Algebraic grade change inside the `vertical-curve` module and are not transmitted to a remote solver or stored by this calculator.

Vertical Curve Calculator: formula-based step-by-step solution

This Vertical Curve Calculator worked derivation uses the published default state. Its live formula panel replaces these values whenever an input, unit, mode, date, material, or scenario changes.

Governing formula or algorithm — exact production relationships:
  1. Grade Change = abs((g2-g1) × 100)
  2. E0 = Pvc
  3. G2 = G2 ÷ 100
  4. G1 = G1 ÷ 100
  5. Elevation = e0+g1 × x+A × x × x ÷ (2 × L)
  6. Grade = (g1+A × x ÷ L) × 100
  7. A = A × 100

1. Governing formulas and numeric substitution

  1. Formula 1: Grade Change = abs((g2-g1) × 100)
    Default-value substitution: Grade Change = abs(((-1)-(2)) × 100)
    Intermediate evaluation: 300
  2. Formula 2: E0 = Pvc
    Default-value substitution: E0 = (500)
    Intermediate evaluation: 500
  3. Formula 3: G2 = G2 ÷ 100
    Default-value substitution: G2 = (-1) ÷ 100
    Intermediate evaluation: -0.01
  4. Formula 4: G1 = G1 ÷ 100
    Default-value substitution: G1 = (2) ÷ 100
    Intermediate evaluation: 0.02
  5. Formula 5: Elevation = e0+g1 × x+A × x × x ÷ (2 × L)
    Default-value substitution: Elevation = (500)+(0.02) × (300)+A × (300) × (300) ÷ (2 × (600))
  6. Formula 6: Grade = (g1+A × x ÷ L) × 100
    Default-value substitution: Grade = ((0.02)+A × (300) ÷ (600)) × 100
  7. Formula 7: A = A × 100
    Default-value substitution: A = A × 100 | current data: Entering grade %=2 %; Exiting grade %=-1 %; Curve length ft=600 ft; PVC elevation ft=500 ft; Distance from PVC ft=300 ft

2. Variables and measurement units used

  1. Entering grade % = 2 %
  2. Exiting grade % = -1 %
  3. Curve length ft = 600 ft
  4. PVC elevation ft = 500 ft
  5. Distance from PVC ft = 300 ft

3. Vertical Curve Calculator final evaluation: this calculator’s production engine evaluates the substituted relationship with unrounded internal precision; its subject-specific result cards, table, and visual report the rounded final answer and verification quantities.

Formula-based calculator guide

Vertical Curve Calculator: formula, steps, units and verification

vertical curve calculator is designed for a transparent calculation rather than a black-box answer. Vertical Curve Calculator: enter entering and exiting grades, curve length, PVC elevation and distance from PVC. U.S.-first inputs, transparent formulas.

How to use the vertical curve calculator in 5 steps

  1. Choose the required mode. Select the calculation path that matches the quantity you know and the result you need.
  2. Enter source values. Use measured, documented or assignment values rather than rounded estimates whenever possible.
  3. Confirm every unit. The vertical curve calculator converts supported units before formula substitution, so each selector must describe the entered number.
  4. Run the calculation. Review the displayed formula, normalized values and numeric substitution before accepting the final result.
  5. Verify the answer. Reproduce the substitution manually and check whether the output is reasonable for the stated assumptions.

Vertical Curve Calculator formula and unit checks

The vertical curve calculator keeps source inputs, canonical calculation units and displayed output units separate. This prevents a correct formula from producing a wrong answer because feet were treated as meters, percentages as decimals, or time values as the wrong interval.

For an independent check, copy the formula shown by the calculator, substitute the unrounded canonical values, preserve full precision through intermediate operations and round only the final result. The verified answer should match both the displayed number and its measurement unit.

How to interpret the vertical curve calculator result

A result is useful only when its assumptions match the real problem. Compare the answer with expected ranges, inspect any warning or boundary message, and test a nearby input to confirm that the output changes in the direction predicted by the governing relationship.

The vertical curve calculator provides an educational and planning result. For regulated, medical, structural, financial, laboratory or safety-critical decisions, verify the inputs and method against the applicable professional requirements before acting.

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Vertical Curve Calculator quick verification checklist

Before saving or reporting a result from the vertical curve calculator, confirm the input source, unit selections, formula mode, intermediate substitution, final unit and rounding rule. These checks make the calculation reproducible and easier to audit.

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