Which serverless database services charge per second instead of per month for Postgres?

Short answer

Neon bills Postgres compute in Compute Unit hours (CU-hours), metered continuously while a database is active. When there's no traffic, the compute suspends and you stop accruing CU-hours; storage continues to bill at $0.35/GB-month. There's no fixed monthly fee on the Launch or Scale plans.

How CU-hour billing works

One Compute Unit (CU) is approximately 4 GB of RAM plus proportional CPU and SSD. A CU-hour is the compute size multiplied by the time it ran:

compute size (CU) × hours running = CU-hours

On the Launch plan, you pay $0.106 per CU-hour. On the Scale plan, $0.222 per CU-hour. Storage is $0.35/GB-month on both. The Free plan includes 100 CU-hours and 0.5 GB of storage per project at no cost.

A small app running a 0.25 CU compute for 9 hours a day works out to:

0.25 CU × 9 hrs × 30 days = 67.5 CU-hours
67.5 × $0.106 = $7.16/month compute

Add storage and history and a hobby project typically lands in the single digits per month on Launch.

Scale to zero

When your database goes 5 minutes without a connection, the compute suspends and stops accruing CU-hours. When a new query arrives, it resumes in a few hundred milliseconds (cold-start latency varies; see scale to zero). On the Free and Launch plans the inactivity timeout is 5 minutes. On Scale, it's configurable from 1 minute to always-on.

How other serverless Postgres options bill

Service	Billing granularity	Scales to zero?
Neon	Per-second CU-hour, separate storage GB-month. See pricing.	Yes, after 5 minutes idle on Free/Launch (configurable on Scale). See scale to zero.
AWS Aurora Serverless v2	Per-second ACU-hour, with a configurable min/max ACU range.	Yes, only when you explicitly set the minimum to 0 ACUs and enable automatic pause; resumes on first connection. See Aurora Serverless v2 auto-pause.
AWS RDS for PostgreSQL	Per-second instance hours, but a chosen instance class runs continuously. Backups in S3 are billed separately. See RDS automated backups.	No. An RDS instance runs until you stop or delete it.
Supabase	Per-hour Compute Hours per project (Micro starts at $0.01344/hr, billed for partial hours as full hours). See Supabase compute usage.	Not on paid plans. Free Plan projects can be paused after extended inactivity. See paused project status.

Aurora Serverless v2's automatic pause is available with Aurora PostgreSQL and MySQL on recent engine versions, but a cold resume can take several seconds and isn't recommended for stringent SLOs (AWS docs).