TheAlgorithms/Python · error · ValueError

Latitude must be between -90 and 90 degrees

Error message

Latitude must be between -90 and 90 degrees

What it means

Raised by lamberts_ellipsoidal_distance() in geodesy/lamberts_ellipsoidal_distance.py when either latitude argument falls outside [-90, 90]. Lambert's formula converts latitudes via tan/radians for the parametric latitude; out-of-range values are geometrically invalid on the WGS84 ellipsoid and rejected before the trigonometry runs.

Source

Thrown at geodesy/lamberts_ellipsoidal_distance.py:71

    ValueError: Longitude must be between -180 and 180 degrees

    >>> from collections import namedtuple
    >>> point_2d = namedtuple("point_2d", "lat lon")
    >>> SAN_FRANCISCO = point_2d(37.774856, -122.424227)
    >>> YOSEMITE = point_2d(37.864742, -119.537521)
    >>> NEW_YORK = point_2d(40.713019, -74.012647)
    >>> VENICE = point_2d(45.443012, 12.313071)
    >>> f"{lamberts_ellipsoidal_distance(*SAN_FRANCISCO, *YOSEMITE):0,.0f} meters"
    '254,351 meters'
    >>> f"{lamberts_ellipsoidal_distance(*SAN_FRANCISCO, *NEW_YORK):0,.0f} meters"
    '4,138,992 meters'
    >>> f"{lamberts_ellipsoidal_distance(*SAN_FRANCISCO, *VENICE):0,.0f} meters"
    '9,737,326 meters'
    """

    # Validate latitude values
    if not -90 <= lat1 <= 90 or not -90 <= lat2 <= 90:
        raise ValueError("Latitude must be between -90 and 90 degrees")

    # Validate longitude values
    if not -180 <= lon1 <= 180 or not -180 <= lon2 <= 180:
        raise ValueError("Longitude must be between -180 and 180 degrees")

    # CONSTANTS per WGS84 https://en.wikipedia.org/wiki/World_Geodetic_System
    # Distance in metres(m)
    # Equation Parameters
    # https://en.wikipedia.org/wiki/Geographical_distance#Lambert's_formula_for_long_lines
    flattening = (AXIS_A - AXIS_B) / AXIS_A
    # Parametric latitudes
    # https://en.wikipedia.org/wiki/Latitude#Parametric_(or_reduced)_latitude
    b_lat1 = atan((1 - flattening) * tan(radians(lat1)))
    b_lat2 = atan((1 - flattening) * tan(radians(lat2)))

    # Compute central angle between two points
    # using haversine theta. sigma =  haversine_distance / equatorial radius
    sigma = haversine_distance(lat1, lon1, lat2, lon2) / EQUATORIAL_RADIUS

View on GitHub (pinned to f5988cc097)

Solutions

1. Ensure both latitudes are within [-90, 90].
2. If lat/lon were swapped at the call site, swap them back — check the longitude error that may follow.
3. Normalize coordinates upstream: clamp or recompute from the source CRS.

Example fix

# before
lamberts_ellipsoidal_distance(lon1, lat1, lon2, lat2)  # swapped order

# after
lamberts_ellipsoidal_distance(lat1, lon1, lat2, lon2)  # lat first

for name, lat in (('lat1', lat1), ('lat2', lat2)):
    if not -90 <= lat <= 90:
        raise ValueError(f'{name}={lat} outside [-90, 90]')
lamberts_ellipsoidal_distance(lat1, lon1, lat2, lon2)

def is_valid_lat(lat: float) -> bool:
    return isinstance(lat, (int, float)) and -90.0 <= lat <= 90.0

try:
    d = lamberts_ellipsoidal_distance(lat1, lon1, lat2, lon2)
except ValueError as exc:
    if 'Latitude' in str(exc):
        raise ValueError(f'bad input coords: {(lat1, lon1, lat2, lon2)}') from exc
    raise

When it happens

Trigger: Calling lamberts_ellipsoidal_distance(95.5, -122.4, 40.7, -74.0) — lat1 > 90. Note the check tests both lat1 and lat2 with one condition, so either bad coordinate raises the same error without saying which.

Common situations: Coordinate-order mixups (lat/lon swapped — longitudes like 40.7 pass as valid latitudes, so swaps often surface here or at the longitude check), missing minus signs on southern-hemisphere latitudes after arithmetic, or unnormalized data from projections emitting values beyond geodetic range.

Related errors

• Longitude must be between -180 and 180 degrees
• Expected a_coeffs to have {self.order + 1} elements for {sel
• n must not be negative
• Depth cannot be less than 0
• The parameter costs should be a list of three integers

AI-assisted analysis of TheAlgorithms/Python@f5988cc097 (2026-08-14). Data as JSON: /api/errors/6443f7d6ad3433f2. Report an issue: GitHub.