An R-T-B based sintered magnet represented by the following formula: uRwBxGayCuzAlqM(100-u-w-x-y-z-q)T where R is composed of light rare-earth element(s) RL and heavy rare-earth element(s) RH, RL is Nd and/or Pr, RH is at least one of Dy, Tb, Gd and Ho, T is Fe, and 10% by mass or less of Fe is capable of being replaced with Co, M is Nb and/or Zr, and u, w, x, y, z, q and 100-u-w-x-y-z-q are expressed in terms of % by mass; said RH accounts for 5% by mass or less of the R-T-B based sintered magnet, the following inequality expressions to being satisfied: 0.20 ≤ x ≤ 0.70 0.07 ≤ y ≤ 0.2 0.05 ≤ z ≤ 0.5 0 ≤ q ≤ 0.1 v = u - (6α + 10β + 8γ), where the amount of oxygen (% by mass) of the R-T-B based sintered magnet is α the amount of nitrogen (% by mass) is β, and the amount of carbon (% by mass) is γ characterised in that when 0.40 ≤ x ≤ 0.70, v and w satisfy the following inequality expressions and: 50 ⁢ w − 18.5 ≤ v ≤ 50 ⁢ w − 14 − 12.5 ⁢ w + 38.75 ≤ v ≤ − 62.5 ⁢ w + 86.125 and, when 0.20 ≤ x < 0.40, v and w satisfy the following inequality expressions and, and x satisfies the following inequality expression: 50 ⁢ w − 18.5 ≤ v ≤ 50 ⁢ w − 15.5 − 12.5 ⁢ w + 39.125 ≤ v ≤ − 62.5 ⁢ w + 86.125 − 62.5 w + v − 81.625 / 15 + 0.5 ≤ x ≤ − 62.5 w + v − 81.625 / 15 + 0.8 with the provisio that the following is excluded: (i) Composition of sintered magnet (% by mass) Nd Fe B Co Ga Cu Al O N C 29.50 bal. 0.91 0.50 0.50 0.10 0.28 0.10 0.05 0.10 31.00 bal. 0.90 0.50 0.50 0.10 0.28 0.10 0.05 0.10 32.40 bal. 0.89 0.50 0.50 0.10 0.28 0.10 0.05 0.10 (ii) Composition of sintered magnet (% by mass) Nd B Ga Cu Co Al Fe 31.00 0.89 0.50 0.10 0.50 0.28 66.73 31.00 0.89 0.50 0.20 0.50 0.28 66.63 R is composed of light rare-earth element(s) RL and heavy rare-earth element(s) RH, RL is Nd and/or Pr, RH is at least one of Dy, Tb, Gd and Ho, T is Fe, and 10% by mass or less of Fe is capable of being replaced with Co, M is Nb and/or Zr, and u, w, x, y, z, q and 100-u-w-x-y-z-q are expressed in terms of % by mass; said RH accounts for 5% by mass or less of the R-T-B based sintered magnet, the following inequality expressions to being satisfied: 0.20 ≤ x ≤ 0.70 0.07 ≤ y ≤ 0.2 0.05 ≤ z ≤ 0.5 0 ≤ q ≤ 0.1 v = u - (6α + 10β + 8γ), where the amount of oxygen (% by mass) of the R-T-B based sintered magnet is α the amount of nitrogen (% by mass) is β, and the amount of carbon (% by mass) is γ characterised in that when 0.40 ≤ x ≤ 0.70, v and w satisfy the following inequality expressions and: 50 ⁢ w − 18.5 ≤ v ≤ 50 ⁢ w − 14 − 12.5 ⁢ w + 38.75 ≤ v ≤ − 62.5 ⁢ w + 86.125 and, when 0.20 ≤ x < 0.40, v and w satisfy the following inequality expressions and, and x satisfies the following inequality expression: 50 ⁢ w − 18.5 ≤ v ≤ 50 ⁢ w − 15.5 − 12.5 ⁢ w + 39.125 ≤ v ≤ − 62.5 ⁢ w + 86.125 − 62.5 w + v − 81.625 / 15 + 0.5 ≤ x ≤ − 62.5 w + v − 81.625 / 15 + 0.8 with the provisio that the following is excluded: (i) Composition of sintered magnet (% by mass) Nd Fe B Co Ga Cu Al O N C 29.50 bal. 0.91 0.50 0.50 0.10 0.28 0.10 0.05 0.10 31.00 bal. 0.90 0.50 0.50 0.10 0.28 0.10 0.05 0.10 32.40 bal. 0.89 0.50 0.50 0.10 0.28 0.10 0.05 0.10 (ii) Composition of sintered magnet (% by mass) Nd B Ga Cu Co Al Fe 31.00 0.89 0.50 0.10 0.50 0.28 66.73 31.00 0.89 0.50 0.20 0.50 0.28 66.63 (i) Composition of sintered magnet (% by mass) Nd Fe B Co Ga Cu Al O N C 29.50 bal. 0.91 0.50 0.50 0.10 0.28 0.10 0.05 0.10 31.00 bal. 0.90 0.50 0.50 0.10 0.28 0.10 0.05 0.10 32.40 bal. 0.89 0.50 0.50 0.10 0.28 0.10 0.05 0.10 (ii) Composition of sintered magnet (% by mass) Nd B Ga Cu Co Al Fe 31.00 0.89 0.50 0.10 0.50 0.28 66.73 31.00 0.89 0.50 0.20 0.50 0.28 66.63