Asphalt shingles is typically 950 lbs/yd3. A 4 yd3 load is about 1.4 to 2.6 tons (typical 1.9 tons). Asphalt shingles are weight-first debris. A full load can hit haul limits before the dumpster looks full, so smaller bins or multi-haul plans are often safer.
Asphalt shingles is usually a weight-first decision surface. Treat volume as secondary after tonnage limits.