Work out rsa key strength instantly with clear inputs, formula shown and shareable results.
RSA security grows very slowly with modulus size because the general number field sieve is sub-exponential: doubling from 2048 to 4096 bits adds only about 28 bits of security while private-key operations get roughly eight times more expensive, since modular exponentiation scales with the cube of the modulus length. That poor trade-off is the main reason new deployments favour elliptic curves.
RSA cost and strength
private-key cost scales as (bits / 2048)^3; security level from NIST SP 800-57: 2048 -> 112 bits, 3072 -> 128 bits, 15360 -> 256 bits
Only where policy demands it. The extra strength is modest and the cost is large; moving to ECDSA P-256 or Ed25519 gives 128-bit security at a fraction of the compute.
The public exponent is normally 65537, which requires only 17 squarings and one multiplication. Verification is therefore hundreds of times faster than signing.