Calculate Degrees From An Old Magnetic North

Calculating the degrees from an old magnetic north to the current magnetic north involves understanding how Earth's magnetic field has shifted over time. This calculation is important for navigation, geology, and historical research. Our calculator provides an accurate way to determine this shift using precise measurements.

What is Magnetic North?

Magnetic north is the direction in which a compass needle points, which is influenced by Earth's magnetic field. Unlike true north (which points to the geographic North Pole), magnetic north can change over time due to natural variations in Earth's magnetic field.

These changes are measured in degrees and can be significant over centuries. For example, in the early 20th century, magnetic north was located in northern Canada, while today it is moving toward Russia. This shift occurs because Earth's magnetic field is generated by the movement of molten iron in the planet's outer core.

How to Calculate Degrees from Old Magnetic North

To calculate the degrees between an old magnetic north position and the current magnetic north, you need the coordinates of both points. The calculation involves determining the angular difference between these two points on Earth's surface.

The process involves:

Obtaining the latitude and longitude of the old magnetic north position.
Obtaining the latitude and longitude of the current magnetic north position.
Using spherical geometry to calculate the angular difference between these two points.

The result will be the number of degrees that magnetic north has shifted from its old position to its current position.

Formula Used

The formula to calculate the degrees between two points on a sphere (like Earth) is:

Δθ = arccos[sin(φ₁)sin(φ₂) + cos(φ₁)cos(φ₂)cos(Δλ)]

Where:

φ₁ is the latitude of the old magnetic north
φ₂ is the latitude of the current magnetic north
Δλ is the difference in longitude between the two points

The result Δθ is the angular difference in degrees between the two points.

Worked Example

Let's calculate the degrees between an old magnetic north position at 80°N, 110°W and the current magnetic north position at 82°N, 100°W.

Convert all angles to radians:
- φ₁ = 80° × (π/180) ≈ 1.400 radians
- φ₂ = 82° × (π/180) ≈ 1.439 radians
- Δλ = (110°W - 100°W) = 10° × (π/180) ≈ 0.174 radians
Apply the formula:
Δθ = arccos[sin(1.400)sin(1.439) + cos(1.400)cos(1.439)cos(0.174)]

Δθ ≈ arccos[0.9848 × 0.9903 + 0.1736 × 0.1411 × 0.9848]

Δθ ≈ arccos[0.9756 + 0.0246] ≈ arccos(0.9999) ≈ 0.035 radians
Convert radians back to degrees:
0.035 radians × (180/π) ≈ 2.01°

The magnetic north has shifted approximately 2.01° from its old position to its current position.

Frequently Asked Questions

Why does magnetic north change over time?: Magnetic north changes because Earth's magnetic field is generated by the movement of molten iron in the planet's outer core. This movement causes the magnetic field to shift and vary over time.
How often should I update my magnetic north calculations?: For most practical purposes, magnetic north changes slowly. However, for precise navigation or scientific research, it's recommended to update calculations every few years to account for the gradual shift.
Can I use this calculator for historical navigation?: Yes, this calculator can be used to determine how magnetic north has shifted over time, which is useful for historical navigation and understanding past magnetic field behavior.
What is the difference between magnetic north and true north?: Magnetic north is the direction a compass points, which is influenced by Earth's magnetic field. True north points to the geographic North Pole. The difference between them is called magnetic declination.
How accurate are the results from this calculator?: The results are as accurate as the input coordinates and the assumptions about Earth's shape. For most purposes, the calculator provides precise results.