Model railway track expansion allowance calculator

Calculate free expansion and equal gap share with your own figures.

Your numbers

Use the units shown. Results update as you change valid inputs.

Use free expansion and equal gap share to compare changes to your inputs. The method and limits below explain the scope.

Examples

Examples

Try the starting example

Track length (metres)
10
Linear expansion coefficient (per kelvin)
1.7e-05
Temperature increase (kelvins)
30
Identical expansion gaps (count)
5
Free expansion (millimetres)
5.1
Equal gap share (millimetres/gap)
1.02

Try another scenario

Track length (metres)
15
Linear expansion coefficient (per kelvin)
2e-05
Temperature increase (kelvins)
40
Identical expansion gaps (count)
6
Free expansion (millimetres)
12
Equal gap share (millimetres/gap)
2
Calculation method

Calculation method

Free expansion (millimetres)

Length metres×coefficient×temperature increase×1000.

Equal gap share (millimetres/gap)

Free expansion/gap count; allocation assumption only.

Symbols and units
a
Track length (metres)
b
Linear expansion coefficient (per kelvin)
c
Temperature increase (kelvins)
d
Identical expansion gaps (count)

Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.

Assumptions & limits

Assumptions & limits

  • Linear free thermal expansion from a user-supplied coefficient; no recommendation for rail fastening or joint design. Supported limits: All numeric inputs and computed intermediates must remain finite. Supported numeric input magnitude is zero or 1e-12 through 1e12 in absolute value; reject values outside this bounded range. All lists/JSON record tables are limited to 100 records unless a stricter bound is stated; reject malformed record arity and wrong member types. All numeric values must be finite. Lists contain at most 100 records; required lists must be nonempty. Rates, probabilities and fractions are entered as fractions, not percentages; fractions must be between 0 and 1. Use a single consistent user-selected currency for all amounts; no exchange-rate conversion.
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