What Does Conv2d Output with 32×32 Input, Kernel 3, Padding 1?

Formula Breakdown

The Conv2d output size formula is:

output_size = floor((input_size - kernel_size + 2 * padding) / stride) + 1

Plugging in the values for 32×32 input:

output = floor((32 - 3 + 2*1) / 1) + 1
output = floor((32 - 3 + 2) / 1) + 1
output = floor(31 / 1) + 1
output = floor(31) + 1
output = 32

So the spatial dimensions go from 32×32 to 32×32.

PyTorch Code Example

import torch
import torch.nn as nn

# Define the Conv2d layer
conv = nn.Conv2d(in_channels=64, out_channels=128, kernel_size=3, stride=1, padding=1)

# Create input tensor: (batch, channels, height, width)
x = torch.randn(1, 64, 32, 32)
output = conv(x)
print(output.shape)  # torch.Size([1, 128, 32, 32])

# Verify with formula
expected = (32 + 2 * 1 - 3) // 1 + 1
print(f"Expected output size: {expected}x{expected}")  # 32x32

Architecture Context

This is the standard “same” convolution preserving spatial dimensions. Used extensively in VGG, ResNet, and DenseNet architectures.

Parameter Count

A Conv2d(64, 128, 3) layer has:

parameters = in_channels * out_channels * kernel_size^2 + out_channels (bias)
parameters = 64 * 128 * 3 * 3 + 128
parameters = 73,856

This layer has 73,856 trainable parameters (73728 weights + 128 bias terms).

Practical Tips

• Memory usage: The output feature map for a single image is 128 × 32 × 32 = 131,072 float values (0.50 MB in float32).
• Batch dimension: Multiply memory by batch size. A batch of 32 uses 16.0 MB for this layer's output alone.
• Same padding rule: For any kernel, setting padding = (kernel_size - 1) / 2 with stride=1 preserves spatial dimensions.

Related Questions

• Conv2d 32×32 Kernel 3 Stride 1 → 30×30
• Conv2d 32×32 Kernel 5 Stride 1 → 28×28
• Conv2d 64×64 Kernel 3 Stride 1 → 64×64
• Conv2d 128×128 Kernel 3 Stride 1 → 128×128
• Conv2d 256×256 Kernel 3 Stride 1 → 256×256