Railway Frog Number Calculator: Frog Angle, Heel Length and Total Length of a Turnout

The geometry of a railway turnout frog.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose what you know: the frog number, the frog angle or the heel length and heel spread.

Enter the heel spread and the toe length.

The calculator gives the frog number, the frog angle, the heel length and the total length of the turnout.

Formulas used

  • FN = \frac{1}{2}\cot\frac{\theta}{2}
  • \tan\frac{\theta}{2} = \frac{1/2}{FN}
  • FN = \frac{\text{Heel length}}{\text{Heel spread}}
  • L = \text{Toe length} + \text{Heel length}

Worked example

With the default numbers in the calculator above:

  1. Frog angle in decimal degrees: 5.72 degrees
  2. Frog angle in degrees, minutes and seconds: 5 deg 43 min 29.32 sec
  3. Heel length: 3110.00 mm
  4. Total length of the turnout: 4930.00 mm

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you know? The frog angle (degrees, minutes, seconds).

  1. Frog angle in decimal degrees: 5.72 degrees
  2. Frog number: 10.00
  3. Frog angle in degrees, minutes and seconds: 5 deg 43 min 29.00 sec
  4. Heel length: 3110.05 mm
  5. Total length of the turnout: 4930.05 mm

Common questions

What is the frog number?

The ratio of the heel length to the heel spread. A frog number 10 spreads the rails 1 unit for every 10 units of length along the frog.

What is the frog angle?

The angle between the centreline of the track and the diverging route at the frog. A bigger frog number is a smaller angle.

What are the toe, heel and heel spread?

The toe is the front end of the turnout, where the switch is. The heel is the back end, where the rails are farthest apart. The heel spread is the perpendicular distance between the two diverging rails at the heel.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any railway engineering text (turnouts and frog numbers). Use the track standard of the railway for the actual turnout geometry.

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