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which projection will be most suitable for the area calculation of polygon which is almost covering the whole northern hemisphere? I am trying to calculate the area of the historic distribution of brown bears so that's why I want to estimate the area of that polygon but its projection is in WGS1984 (Geographic Coordinate System) and in this projection, I cant calculate the area so I have to change its projection to Projected Coordinate system "GCS to PCS" and now I'm confused and I don't know which projection would be likely to cover Whole Northern Hemisphere!

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I would try Lambert azimuthal equal-area https://pro.arcgis.com/en/pro-app/latest/help/mapping/properties/lambert-azimuthal-equal-area.htm

Distortion

Lambert azimuthal equal-area is an equal-area (equivalent) projection. Shapes, directions, angles, and distances are generally distorted. Scale and directions are true only at the center of the projection. The scale decreases with the distance from the center along the radii and increases from the center perpendicularly to the radii, resulting in small shapes compressed radially from the center and elongated perpendicularly. The general pattern of distortion is radial.

Usage

Although the Lambert azimuthal equal-area projection can display the entire globe, its practical usage is typically limited to a hemisphere. This projection is most commonly used for thematic mapping of polar regions. The oblique aspect is sometimes used for individual land masses that are symmetrically proportioned, either round or square.

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