Rafter Length Calculator

Length B, mm

Length S, mm

Set the height "H"

Set roof angle "a"

Height H, mm

Angle a, °

Snow load

Wind load

Roofing material

Permanent load , kg/m²

Rafter spacing D, mm

Wood grade

Deflection stiffness

Set the h/b ratio

Set width b

Ratio h/b

Width b, mm

Name	Result
Rafter length	{{dlina_L}} mm
Roof angle	{{ygol}} °
Load area	{{F}} m²
Overhang length along the rafter	{{a_over_mm}} mm
Span between supports along the rafter	{{Lspan_mm}} mm
Design snow load	{{sneg_r}} kg/m² ≈ {{sneg_r_kn}} kN/m²
Design wind load	{{veter_r}} kg/m² ≈ {{veter_r_kn}} kN/m²
Design permanent load	{{post_r}} kg/m² ≈ {{post_r_kn}} kN/m²
Total design load per rafter	{{nagr_r_obschaya}} kg/m² ≈ {{nagr_r_obschaya_kn}} kN/m² or {{nagr_r_obschaya_F}} kg
Design line load on the rafter	{{q_knm}} kN/m
Bending moment in span	{{Mspan}} N*mm
Bending moment from overhang	{{Mover}} N*mm
Maximum bending moment M	{{moment}} N*mm
Required section modulus W	{{W}} mm³
Deflection limit	{{deflim_txt}}
Allowable deflection	{{flim_mm}} mm
Calculated deflection in span	{{f_mm}} mm
Required rafter section h×b	{{visota}}x{{shirina}} mm

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About Rafter Length Calculation

The results are approximate. Before use, verify the calculations against the applicable standards and consult a specialist. The developer is not responsible for the consequences of use without project verification.

This calculator performs a rafter member calculation based on roof geometry and specified loads. It determines the rafter length, roof pitch angle, tributary area per rafter, design loads (snow, wind, permanent), line load, bending moments, required section modulus, and a recommended rectangular timber section h×b.

The calculation is suitable for preliminary sizing and for assessing how roof angle, rafter spacing, snow load, and wind load affect internal forces and deflection.

Guidelines and recommendations

Geometry and rafter length. First, the roof slope angle a and the geometric rafter length L are determined. With a given rise H (mm), the angle is found from the ratio of rise to the horizontal projection (B+S) (mm). With a given angle a, the length is found using the cosine relation. A small allowance of about 1% is added to the resulting length for trimming and real-world fitting.

a = arctan(H / (B + S))

L = sqrt((B + S)² + H²)

L = (B + S) / cos(a)

Tributary area per rafter. The roof area carried by one rafter is computed as the rafter length L (mm) multiplied by the rafter spacing D (mm), converted to m². This value is used to convert an area load (kg/m² or kN/m²) into a total load per rafter (kg).

F = (L · D) / 1 000 000

Snow shape coefficient. The effect of roof pitch on snow is accounted for by the shape coefficient μ, which decreases as the angle increases. A piecewise linear relationship is used as a practical approximation for pitched roofs.

μ = 1 for a ≤ 30°

μ = 0 for a ≥ 60°

μ = (60 − a) / 30 for 30° < a < 60°

Design snow load. From the specified characteristic snow load S₀ (kg/m²), a design value is formed using the factor 1.4 and the shape coefficient μ. This reflects an approach where the snow action is increased by a reliability factor and adjusted for roof shape.

S = 1.4 · S₀ · μ

Design wind load. Wind is specified as an input value W (kg/m²) or (kN/m²). It is then converted to a design value using the factor 1.4 and a simplified aerodynamic multiplier 0.8 for a roof slope. In practice, wind pressure per EN 1991-1-4 may vary by roof zones, so the calculator uses an averaged scheme for preliminary assessment.

W_d = 1.4 · W · 0.8

Design permanent load. The permanent load is formed as the sum of the selected roof covering self-weight G_roof (kg/m²) and an additional permanent load G_add (kg/m²) for other roof build-up layers entered separately. The factor 1.1 is then applied.

G = 1.1 · (G_roof + G_add)

Total design area load. Snow, wind, and permanent loads are summed into a total design load per 1 m² of roof area. The calculator also shows an equivalent load per rafter using the tributary area F.

p = S + W_d + G

P = p · F

Conversion to line load. For bending calculations, the rafter is treated as a member under a uniformly distributed line load derived from the area load. With rafter spacing D (mm), the mm → m conversion is applied.

q = p · (D / 1000)

Unit conversion. If the load is entered in kN/m², it is converted to kg/m² using 1 kN/m² ≈ 101.97 kg/m². For displaying the line load in kN/m, the approximation 1 kgf ≈ 9.81 N is used.

1 kN/m² ≈ 101.97 kg/m²

q_kN/m = q_kg/m · 9.81 / 1000

Eave overhang and design span. The horizontal overhang S (mm) is converted into the overhang length along the rafter a_over using the roof angle. The design span between supports along the rafter is taken as the rafter length minus the overhang. If this becomes negative, it is taken as 0.

a_over = S / cos(a)

L_span = max(0, L − a_over)

Bending moment. The calculator compares two cases: span action and cantilever overhang action. For the overhang, the cantilever formula under uniform load is used. For the span, a simplified estimate is applied that accounts for the influence of the overhang on moment distribution. The larger value is taken as the design bending moment.

M_over = q · a_over² / 2

M = max(M_span, M_over)

Required section modulus. From the maximum moment, the required section modulus W (mm³) is obtained using the allowable bending stress σ (N/mm²), selected by timber strength class. For a rectangular section, the standard section modulus relation is used.

W = M / σ

W = b · h² / 6

Deflection check. The deflection limit is set as L/200, L/250, or L/300. The allowable deflection is w_lim = L_span / k, where k is 200, 250, or 300. The required second moment of area is estimated for a simply supported member under uniform load using the timber modulus of elasticity E = 11000 N/mm².

w_lim = L_span / k

I_req = 5 · q · L_span⁴ / (384 · E · w_lim)

Section selection h×b. The section is selected to satisfy two conditions: strength via the required W and stiffness via the required I. If a ratio r = h/b is set, the width is expressed through the height. If a fixed width b is set, the required height is computed. The final height is taken as the larger value from the two conditions.

h = (6 · W · r)^1/3 and b = h / r

h = (12 · r · I_req)^1/4 and b = h / r

h = sqrt(6 · W / b) for a fixed width b

h = (12 · I_req / b)^1/3 for a fixed width b

Deflection verification for the chosen section. After initial selection, the actual deflection is calculated for the chosen b and h. If the deflection exceeds the limit, the section height is increased automatically until the deflection condition is satisfied.

I = b · h³ / 12

w = 5 · q · L_span⁴ / (384 · E · I)

Practical reference ranges. Common rafter spacing values are 600-900 mm. For rectangular timber sections, ratios h/b around 1.5-3 are widely used. Increasing the roof angle can reduce the snow component via μ, but it also changes rafter length and the overhang geometry, so bending moments and deflection should be assessed together.

Standards. Load assumptions can be cross-checked against Eurocode principles. For snow actions use EN 1991-1-3. For wind actions use EN 1991-1-4. For timber members and checks of strength and stiffness use EN 1995-1-1. In a real project, coefficients and combinations are taken from the National Annex and the actual site conditions.

FAQs

Why does the snow load decrease for a steep roof?

The calculation uses the shape coefficient μ, which reflects that snow is less likely to accumulate on steep slopes and is more often blown off or slides down. The adopted rule is 1 at 30° and below, 0 at 60° and above, with a linear transition between. This is a simplified model for preliminary rafter sizing.

Why are moments from the span and from the overhang both checked?

A rafter works both as a simply supported member between supports and as a cantilever over the eave. With a long overhang, the maximum moment may be governed by the cantilever action near the support. With a small overhang, the span action more often governs. Therefore, the design moment is taken as the larger of the two.

How is an area load (per m²) converted into a rafter load?

First, the total design area load p (kg/m² or kN/m²) is formed. It is then converted into a line load using the rafter spacing D, which corresponds to the load carried by a roof strip whose width equals the spacing. Additionally, the load per rafter is shown via the tributary area F.

What do the deflection limits L/200, L/250, L/300 mean?

They define the allowable deflection as a fraction of the span between supports along the rafter. A larger denominator means a stricter stiffness requirement and typically a larger required section. The calculator estimates the required second moment of area first, then checks the actual deflection of the selected section.

Which results are preliminary and what should be checked separately?

The results reflect an analysis of a rafter under a simplified uniform load model and typical factors. In practice, connection design, bearing stresses at supports, bracing, local stability, load combinations, and wind zoning per EN 1991-1-4 are usually verified separately. For complex roof geometry or higher responsibility structures, the rafter design should be checked to Eurocode with the applicable National Annex.