Concerns raised by members of the public with the NSPCC in Scotland included worries about young people who were victims of physical or sexual abuse, children living in squalid conditions, and hungry toddlers.
New figures from the free, 24-hour helpline show operators took 1,722 calls serious enough to be referred to the authorities in 2015/16, compared with 1,091 referrals in 2012/13.
The charity said the rise in referrals shows the public is increasingly unwilling to turn a blind eye to potential abuse or neglect of children, following high-profile abuse scandals.
The new statistics show physical abuse referrals from the helpline increased 49% from 259 in 2012/13 to 389 in 2015/16.
Sexual abuse referrals rose by 30% over the same period, from 144 to 187, and neglect referrals jumped by 61% from 499 to 803.
Overall calls to the helpline increased by 22% to six a day in 2015/16, when there were 2,297 calls compared with 1,885 in 2012/13 when the Jimmy Savile abuse allegations first came to light.
Matt Forde, national head of service for NSPCC Scotland, said: “These figures reveal a nation that is more alive to the issues of child abuse following recent high-profile scandals and the ongoing investigation into non-recent child abuse.
“They have become increasingly concerned and aware of the tell-tale signs of abuse and neglect in children and our helpline is an invaluable service for people worried about the safety of a young person.
“But when people are worried, and feel they need to speak to someone, they can be reassured they will be listened to and taken seriously.”
The helpline provides adults with a place they can get advice and support, share their concerns about a child or get general information about child protection.
Adults can contact the helpline 24 hours a day, 365 days a year, on 0808 800 5000, by texting 88858 or by visiting www.nspcc.org.uk.
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