There are no strict rules for buying a replacement lamp shade, but there are guidelines. Measure both the lamp and the potential replacement shades. Ideally, you should bring the lamp base with you when shop for a replacement shade, but even then, knowing what measurements you're looking for will narrow your search.
Measure the height of the lamp's base, excluding the hardware that holds up the shade and light bulb. Martha Stewart Living says that lamp shades look best when they are 2/3 as tall as the lampshade. Multiply the height of the lamp base by .66 to calculate the approximate height of your replacement shade.
Measure the widest point of the lamp base and write down the measurement. Martha Stewart Living recommends getting a replacement shade that is slightly wider than the base's widest point. Add 2 inches to the width of the lamp base to calculate the approximate width of the bottom of the replacement lamp shade.
Measure the width of the widest part of light bulb you will use in the lamp. For safety, at least 1 inch of clearance should be between the light bulb and the shade. If the bulb is 100 watts or more, clearance should be 2 inches. If your light bulb is less than 100 watts, add 2 inches to the bulb width measurement to calculate the minimum width of the top of the lamp shade. If the light bulb is 100 watts or more, add 4 inches to the bulb width measurement.
Measure the distance between the spot on the lamp base where the shade will be attached and the top shoulder of the base. The distance between the replacement shade's hardware (attached to the base) and the bottom of the shade should be less than this measurement. Otherwise, the lamp shade will look too long.
Measure the distance between the spot on the lamp base where the shade will be attached and the bottom of the base's hardware (electrical fittings). The distance between the replacement shade's hardware and the bottom of the shade should be greater than this measurement. Otherwise, the hardware will be visible.
Take your tape measure with you to the store when shopping for a replacement lamp shade.
If your lamp shade is closer to the light bulb than recommended, it increases the risk of heat damage to the lamp shade, as well as fire.