The formulas used most in sheet metal layout, on one page to print. Lengths in one unit throughout; angles in degrees.
Round work and true lengths
What
Formula
Mean diameter of a rolled part
d = outside diameter − thickness
Developed length of a rolled part
π × d
True length of a sloping line
√(plan length² + height²)
Chord of n equal parts of a circle
2 × radius × sin(180° ÷ n)
Right cone: R and r the end radii, h the height
What
Formula
Slant height
L = √(h² + (R − r)²)
Large arc radius
A = L × R ÷ (R − r)
Small arc radius
B = L × r ÷ (R − r)
Sector angle
θ = 360° × (R − r) ÷ L
Segmented elbow: R the bend radius, r the pipe radius
What
Formula
Angle at each joint
θ = bend angle ÷ joints
Ordinate of a gore
y = (R + r × cos φ) × tan(θ ÷ 2)
Press brake bends: A the bend angle, IR the inside radius, T the thickness, K the K-factor
What
Formula
Bend allowance
BA = A × π ÷ 180 × (IR + K × T)
Outside setback
OSSB = tan(A ÷ 2) × (IR + T)
Bend deduction
BD = 2 × OSSB − BA
Flat length of one bend
leg 1 + leg 2 − BD (legs to the outside)
The K-factor depends on the material, the tooling and the ratio of radius to thickness. Values from about 0.33 to 0.5 are common; a test bend gives the true figure for your brake.