Band Saw Blade Length Calculator

How it works

A band saw blade is a belt. On two wheels of the same diameter it runs straight between the wheels on both sides, each run as long as the distance between the wheel centers, and wraps half of each wheel, so its length is twice the center distance plus one wheel circumference.

When the wheels differ, the straight runs are tangent to both wheels and tilt toward the smaller one. The blade then wraps more than half of the larger wheel and less than half of the smaller. The page uses the exact open-belt length; the simpler π × (D1 + D2) ÷ 2 + 2C formula is slightly short, by about (D1 − D2)² ÷ (4C).

On three wheels of the same diameter, each straight run is parallel to the line joining two wheel centers and as long as it, and the wraps add up to one full turn, so the length is the sum of the three center distances plus one circumference.

Every point of the blade moves at the rim speed of the wheels: the circumference of a wheel times its RPM.

Formula

two equal wheels      L = 2C + π × D
three equal wheels    L = C₁₂ + C₂₃ + C₃₁ + π × D
two unequal wheels    L = 2√(C² − (r₁ − r₂)²) + r₁(2π − θ) + r₂θ,   θ = 2 arccos((r₁ − r₂) ÷ C), r₁ ≥ r₂
                        ≈ 2C + π(D₁ + D₂) ÷ 2 + (D₁ − D₂)² ÷ (4C)
blade speed (ft/min)  = π × D(in) × RPM ÷ 12

Example

Two 14 in wheels with their centers 24 in apart take a blade 2 × 24 + π × 14 = 91.98 in long, about 92 in to the nearest 1/16. At a wheel speed of 800 rpm the blade moves at π × 14 × 800 ÷ 12 = 2,932 ft/min (14.90 m/s).

A 12 in and a 10 in wheel 30 in apart take 94.59 in; three 10 in wheels with centers 20, 18 and 16 in apart take 54 + 10π = 85.42 in.

Assumptions and limitations

• The center distance is the one at which the blade will run, with the upper wheel at its tensioning position; saws allow a range of travel, and the length a saw takes is set by its manufacturer. The result is geometry, not a substitute for the saw manual's blade length.
• The blade is treated as a line running on the wheel diameter entered; blade thickness and tire crown are ignored.
• Three-wheel saws are taken to have three wheels of the same diameter with the blade wrapping the outside of all three.
• Blade speed uses the wheel RPM entered, which the page does not check against the saw's rating.

Frequently asked questions