The Real-Return Shortcut Most Calculators Use Is Off by 461 bps in Emerging-Market Inflation

Irving Fisher's 1930 identity says r = (1+i)/(1+π) − 1. Almost every consumer 'real return' calculator on the web ships the first-order shortcut r ≈ i − π. At G7 inflation the shortcut is fine; at 50% nominal / 30% inflation it overstates by 461.5 basis points. The cross-product term r·π is the error, and it scales linearly with the product of the two rates.