Learn: Vertical-curve K value
The K value of a parabolic vertical curve expresses how much curve length is provided per one percentage-point change in grade. A larger K means a more gradual change for the same grade difference.
What the formula is saying
Calculate the absolute algebraic difference between the two endpoint grades as percentage points, call it A, and divide curve length L by A. This calculator starts with A already supplied.
Read the symbols in plain language
- L
- Curve length
Curve length. Dividing length by the grade difference gives the vertical-curve K value in the stated convention.
mMetres measure length; 1 m = 1000 mm.
- A
- Algebraic grade difference
Magnitude of the difference between two signed grades in percentage points: +2% to −2% gives 4, not 0.04.
percentage pointsUse percentage points as the base unit shown here. L is in m; A is a grade difference in percentage points, not a decimal slope. For +2% and −2%, A is 4, not 0.04. K is m/% in the usual highway notation.
- K
- Result to find
Vertical-curve K value. Dividing length by the grade difference gives the vertical-curve K value in the stated convention.
m/%
Sort out the units first
L is in m; A is a grade difference in percentage points, not a decimal slope. For +2% and −2%, A is 4, not 0.04. K is m/% in the usual highway notation.
Assumptions before calculating
Assume a parabolic vertical curve with a nonzero absolute grade difference and consistent grade percentages. Use positive length and A; the absolute value has already removed the crest-or-sag sign.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
Read the supplied values as one complete study case. Find K and explain the result in the stated output unit.
- L · Curve length
- 200 m
- A · Algebraic grade difference
- 4 percentage points
Identify the absolute grade difference
Use whole percentage points, such as four for a change from plus two to minus two percent.
(4) = 4 percentage pointsFind length per percentage-point change
Dividing length by the grade difference gives the vertical-curve K value in the stated convention.
(200) ÷ (4) = 50 m/%
Does this worked answer make sense?
Multiplying K by the stated A must recover L. For the same curve length, doubling the grade difference halves K.
A second worked example — different values
A second case uses different data. Predict which way the answer will change, then calculate it without reusing the first answer.
- L · Curve length
- 180 m
- A · Algebraic grade difference
- 3 percentage points
Identify the absolute grade difference
Use whole percentage points, such as four for a change from plus two to minus two percent.
(3) = 3 percentage pointsFind length per percentage-point change
Dividing length by the grade difference gives the vertical-curve K value in the stated convention.
(180) ÷ (3) = 60 m/%
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Solve this separate case yourself. Use only the values below; the two worked examples use different data. Give the requested result in the selected unit.
- L · Curve length
- 240 m
- A · Algebraic grade difference
- 6 percentage points
Find: Learn: Vertical-curve K value
A hint, not the answer
Calculate the absolute algebraic difference between the two endpoint grades as percentage points, call it A, and divide curve length L by A. This calculator starts with A already supplied.
L is in m; A is a grade difference in percentage points, not a decimal slope. For +2% and −2%, A is 4, not 0.04. K is m/% in the usual highway notation.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Identify the absolute grade difference
Use whole percentage points, such as four for a change from plus two to minus two percent.
(6) = 6 percentage pointsFind length per percentage-point change
Dividing length by the grade difference gives the vertical-curve K value in the stated convention.
(240) ÷ (6) = 40 m/%
Avoid the common trap
Do not enter the signed sum of grades instead of their absolute algebraic difference. Do not divide the percentage-point input by 100 in this convention.
When this method applies — and when it does not
This calculation reports an existing curve’s K; it does not select an acceptable minimum. Crest and sag sight-distance criteria, comfort, drainage and local standards differ. If the grades are identical, A = 0 and this quotient is undefined.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Reading focus: Vertical-curve K value. Horizontal/vertical alignment and sight-distance context. The geometry identities here are not a selection of a compliant speed, radius or K value for a real road.
Lesson updated: · Both examples and the separate practice case are checked against an independent high-precision numerical implementation. This verifies arithmetic for the stated model, not engineering certification.