Civil Engineering

Footing Design Calculator

Design an isolated pad footing to IS 456. Enter the column load, footing plan size, effective depth and safe bearing capacity, and this calculator returns the bearing pressure distribution, the punching shear check on the critical perimeter, the one-way shear check, the factored cantilever moments and the flexural steel required in both directions. Where the load is eccentric it also works out whether the base stays in full contact with the soil, and switches to the exact partial-contact pressure when it does not.

IS 456:2000 Cl.34 · Cl.31.6.3 punching · Cl.26.5.2.1 minimum steel

🔨 Footing Inputs

Inputs convert when you switch. Results are always reported in SI — see the note under the results.

Service Column Load P (kN)

Safe Bearing Capacity q_a (kN/m²)

Column Width c_b (mm)

Column Depth c_d (mm)

Footing Width B (m)

Footing Length L (m)

Effective Depth d (mm)

Eccentricity e_x about B (m)

Leave at 0 for a concentrically loaded pad.

Eccentricity e_y about L (m)

Both non-zero gives biaxial bending — read the caveat below.

Concrete Grade f_ck

Steel Grade f_y

📊 Design Checks

Press Design Footing to run the checks.

ƒ Governing Formulae

Bearing pressure, resultant inside the kern

q_avg = P / (B · L)
q_max = q_avg · (1 + 6e_x/B + 6e_y/L)
q_min = q_avg · (1 − 6e_x/B − 6e_y/L)

Bearing pressure, resultant outside the kern (uniaxial)

valid only while 6e_x/B + 6e_y/L ≤ 1
beyond that: q_max = 2P / [ 3L (B/2 − e_x) ]
contact length = 3 (B/2 − e_x)

Punching (two-way) shear — IS 456 Cl.31.6

b₀ = 2 [ (c_b + d) + (c_d + d) ]
V_punch = 1.5P − 1.5 q_avg (c_b + d)(c_d + d)
τ_v = V_punch / (b₀ · d)
k_s = min(1.0, 0.5 + β_c) β_c = short side / long side of column
τ_c = k_s · 0.25 √f_ck

Flexure and one-way shear

M_u = 1.5 · q_max · a² / 2 a = (B − c_b) / 2
A_st = M_u / (0.87 f_y · 0.9d)
A_st,min = p_t,min · D p_t,min = 0.12% for f_y ≥ 500, else 0.15%
τ_v,one-way = 1.5 q_max (a − d) / d

P — service (unfactored) axial load from the column

B, L — footing plan dimensions; B is the direction e_x acts about

c_b, c_d — column plan dimensions

d — effective depth to the centroid of tension steel

D — overall depth, taken here as d + 50 mm

q_a — safe (allowable) bearing capacity of the soil, a service-level value

a — cantilever projection from the column face to the footing edge

τ_v, τ_c — applied and permissible shear stress

1.5 — partial load factor applied to the service load for the strength checks; bearing is checked unfactored

Assumptions built into this calculation. The lever arm is taken as 0.9d rather than solved from the stress block, which is slightly conservative for lightly reinforced sections. Overall depth is effective depth plus 50 mm, so change your effective depth if your cover differs. Self-weight of the footing and the soil above it is not added to P — add it yourself if your bearing check needs it, typically 10 to 15 percent of the column load. Permissible one-way shear stress follows the IS 456 Table 19 expression using the steel actually provided.

📝 Worked Example 1 — Concentric Pad Footing

Given

A 400 × 400 mm column carrying a service load of 1000 kN on soil with a safe bearing capacity of 150 kN/m². Trial footing 3.0 × 3.0 m with 450 mm effective depth, M25 concrete and Fe500 reinforcement, load applied concentrically.

Step 1 — plan area and bearing pressure

Area required = 1000 / 150 = 6.67 m², and 3.0 × 3.0 provides 9.00 m².
q = 1000 / 9 = 111.11 kN/m², comfortably under the 150 kN/m² allowable. With no eccentricity q_max and q_min are equal and the base is in full contact.

Step 2 — punching shear on the critical perimeter

The perimeter sits d/2 = 225 mm from each column face, so the punched area is 0.85 × 0.85 m and
b₀ = 2 × (0.85 + 0.85) = 3400 mm
V_punch = 1.5 × 1000 − 1.5 × 111.11 × 0.85 × 0.85 = 1379.6 kN
τ_v = 1379.6 / (3.400 × 0.450 × 1000) = 0.902 MPa
The column is square so β_c = 1.0 and k_s = 1.0, giving τ_c = 1.0 × 0.25√25 = 1.250 MPa. Punching passes at 72 percent utilisation.

Step 3 — flexure at the column face

Cantilever a = (3.0 − 0.4) / 2 = 1.30 m
M_u = 1.5 × 111.11 × 1.30² / 2 = 140.83 kN·m/m
A_st = 140.83 × 10⁶ / (0.87 × 500 × 0.9 × 450) = 799 mm²/m
Minimum steel = 0.12% × 500 mm overall depth = 600 mm²/m, so the calculated area governs.

Step 4 — one-way shear

The critical section is d from the column face, leaving 1.30 − 0.45 = 0.85 m of overhang.
τ_v = 1.5 × 111.11 × 0.85 / (0.450 × 1000) = 0.315 MPa against a permissible 0.918 MPa. Passes with a wide margin, as expected — punching governs.

Bearing q_max = 111.11 kN/m² ≤ 150 — PASS

Punching shear 0.902 ≤ 1.250 MPa — PASS

One-way shear 0.315 ≤ 0.918 MPa — PASS

Reinforcement 799 mm²/m each way, above the 600 mm²/m minimum

Overall verdict — PASS, full contact on the base

These are the calculator's default inputs. Press Design Footing without changing anything and you should get exactly these figures back. Note the pattern: punching runs at 72 percent while one-way shear sits at 34 percent, which is the usual signature of a square column on a square pad. If you need to trim the depth, punching is the check to watch.

⚠ Worked Example 2 — When the Base Lifts Off

Given

The same 3.0 × 3.0 m footing and 400 mm column, 1000 kN service load, but now with a moment at the base giving an eccentricity e_x = 0.90 m. Soil this time is stiffer, q_a = 350 kN/m².

Step 1 — is the resultant inside the kern?

The kern limit is B/6 = 3.0 / 6 = 0.500 m. With e_x = 0.90 m, 6e_x/B = 1.80, which is greater than 1. The resultant is outside the middle third. The linear pressure diagram would require the soil to pull down on the heel, which it cannot do, so contact is partial.

Step 2 — the pressure the linear formula would report

q_avg(1 + 6e/B) = 111.11 × 2.80 = 311.11 kN/m², with a fictitious q_min of −88.89 kN/m². Against q_a = 350 this reads as a comfortable pass.

Step 3 — the pressure that actually develops

q_max = 2 × 1000 / [3 × 3.0 × (1.5 − 0.9)] = 2000 / 5.4 = 370.37 kN/m²
Contact length = 3 × (1.5 − 0.9) = 1.800 m of the 3.000 m base — 40 percent of the footing is off the ground.

The linear formula under-predicts the peak pressure by 19 percent.

Bearing: 370.37 > 350 kN/m² — FAILS, where the linear value said pass

Flexural moment rises from 394.33 to 469.44 kN·m/m

Reinforcement rises from 2238 to 2665 mm²/m — 19 percent more steel

One-way shear goes from 0.881 MPa (passing) to 1.049 MPa against 0.918 permissible — FAILS

What to do about it

Widen the footing until B/6 exceeds the eccentricity, shift the footing so the centroid moves under the resultant, or tie the footing to adjacent foundations with a strap or plinth beam so the moment is shared. Simply accepting the linear number is not one of the options.

Biaxial eccentricity is a special case. When both e_x and e_y put the resultant outside the kern, the partial contact area is a triangle or trapezoid with no closed-form solution, and this calculator says so explicitly rather than quoting a number it cannot stand behind. It reports the linear value, flags it as under-predicting, and fails the verdict. For that case use a numerical contact-area solution or enlarge the footing until the resultant comes back inside the kern.

📏 Inputs, Units and Accepted Ranges

Input	SI unit	Imperial unit	Accepted	Notes
Service column load P	kN	kip	> 0	Unfactored; footing self-weight not included
Safe bearing capacity q_a	kN/m²	ksf	> 0	Service-level allowable value, not ultimate
Column c_b, c_d	mm	in	> 0, less than B and L	Sets β_c and therefore k_s
Footing B, L	m	ft	> 0, greater than the column	B is the direction e_x acts about
Effective depth d	mm	in	> 0	Overall depth assumed as d + 50 mm
Eccentricity e_x, e_y	m	ft	\|e_x\| < B/2, \|e_y\| < L/2	Beyond B/2 the footing overturns and is rejected
Concrete grade f_ck	MPa	—	M20 – M40	Drives the permissible punching stress
Steel grade f_y	MPa	—	Fe415, Fe500, Fe550	Fe500 and above use 0.12% minimum steel, Fe415 uses 0.15%

📚 Reference Tables

Permissible punching shear stress τ_c = k_s · 0.25√f_ck — IS 456 Cl.31.6.3, shown for a square column where k_s = 1.0

Concrete grade	√f_ck	τ_c at k_s = 1.0, MPa
M20	4.472	1.118
M25	5.000	1.250
M30	5.477	1.369
M35	5.916	1.479
M40	6.325	1.581

For a rectangular column, k_s = 0.5 + β_c capped at 1.0, where β_c is the ratio of the short side to the long side. A 300 × 900 column gives β_c = 0.333 and k_s = 0.833, cutting the permissible stress by a sixth.

Indicative safe bearing capacities — IS 1904 / IS 6403 order of magnitude

Soil	Typical SBC, kN/m²	Notes
Soft clay	50 – 100	Settlement usually governs, not bearing
Medium clay	100 – 150	Check long-term consolidation
Stiff clay	150 – 250	Watch shrink–swell in black cotton soil
Loose sand	100 – 150	Sensitive to water table position
Medium to dense sand	200 – 450	Bearing rarely governs at this range
Soft rock / weathered rock	450 – 900	Depends heavily on RQD and jointing
Hard rock	> 1500	Concrete bearing may govern instead

Indicative only. Use the value from your own geotechnical investigation report; these figures are for sanity-checking an input, not for design.

Minimum reinforcement — IS 456 Cl.26.5.2.1, applied to the overall depth D

Steel grade	p_t,min	A_st,min at D = 500 mm	A_st,min at D = 750 mm
Mild steel / Fe415	0.15 %	750 mm²/m	1125 mm²/m
Fe500 and above	0.12 %	600 mm²/m	900 mm²/m

Which check governs the depth — typical utilisation for a square column on a square pad

Check	Critical section	Typical utilisation	Governs when
Bearing pressure	Whole plan area	60 – 90 %	Weak soil; sets the plan size, not the depth
Punching shear	Perimeter at d/2 from column face	60 – 90 %	Almost always — sets the depth
One-way shear	Full width at d from column face	25 – 45 %	Long narrow footings, large projections
Flexure	Column face	Sets steel, not depth	Rarely governs depth in pad footings

❓ Frequently Asked Questions

How do you design an isolated footing as per IS 456?

You size the plan area first, from the service column load divided by the safe bearing capacity of the soil. You then pick a trial depth and check it against punching shear on a perimeter half the effective depth from the column face, and against one-way shear on a section one effective depth from the column face. Finally you calculate the cantilever moment at the column face and provide flexural steel for it, subject to the minimum reinforcement percentage. Depth is almost always governed by shear rather than by moment.

What is the difference between one-way shear and punching shear in a footing?

One-way shear treats the footing as a wide beam and checks a full-width vertical section taken one effective depth from the column face. Punching shear, also called two-way shear, checks a closed perimeter drawn half an effective depth out from all four column faces, where the column tries to punch a cone through the slab. Punching almost always governs for a square column on a square footing, because the same load is resisted by a much shorter critical length.

Why does my footing fail when the eccentricity exceeds B/6?

Beyond B/6 the resultant leaves the middle third of the base and the soil would have to pull down on the footing to keep the pressure diagram linear, which soil cannot do. The base lifts off over part of its length, contact becomes partial and the peak pressure rises above what the standard q = P/A times one plus six e over B expression predicts. This calculator detects that condition and switches to the exact partial-contact expression instead of reporting the invalid linear value.

What is the minimum reinforcement for a footing slab?

IS 456 clause 26.5.2.1 sets the minimum reinforcement in a slab at 0.12 percent of the gross cross-sectional area for high yield strength deformed bars of grade Fe500, and 0.15 percent for mild steel. The percentage applies to the overall depth of the section, not the effective depth, so a footing with 450 mm effective depth and 50 mm cover is checked against a 500 mm overall depth.

How do you find the effective depth of an isolated footing?

Effective depth is the distance from the compression face down to the centroid of the tension reinforcement, so it equals the overall depth less the cover and less half the bar diameter. In practice you assume a trial depth, test it against punching shear first because that usually governs, then against one-way shear, and increase it until both pass. Overall depth is normally taken as effective depth plus about 50 to 75 mm depending on the cover required for the exposure class.

🔗 Related Tools

← All Civil Engineering Calculators

Footing Design Calculator — multicalci.com. Results follow IS 456:2000 with the assumptions stated above and are indicative only. Footing self-weight and soil surcharge are not included in the bearing check. All foundation design must be checked by a qualified structural engineer against a site-specific geotechnical report.